Was Stalin during his last months (the time of the "Doctors' Plot") planning to have Soviet Jews deported to Siberia?
Well, there definitely was an "open letter" going around, to be published in *Pravda*, which prominent Soviet Jews were being pressured to sign, which acknowledged the strong feelings aroused by the Doctors' Plot, and in order to save the country's Jews from the "wrath of the people", asked Stalin to send the country's Jews to Siberia and Birobidjan where they would be housed and protected. Ilya Ehrenburg clearly, though cautiously, referred to this open letter in his memoirs:
"I will omit the story of how I tried to prevent the appearance in print of a certain collective letter. Happily, the project, which was absolutely insane, did not come about. I thought at the time that I dissuaded Stalin with my letter; now it seems to me the whole business was delayed and Stalin did not succeed in doing what he wanted to do. This is history, of course, a chapter of my biography, but I believe the time has not yet come for me to say more."
As Ehrenburg indicated, he not only refused to sign the "open letter" but sent a letter objecting to it to Stalin, a translation of which is provided in Joshua Rubenstein's *Tangled Loyalties: The Life and Times of Ilya Ehrenburg*, pp. 274-5, where Ehrenburg shrewdly argued that the open letter and the proposal would actually strengthen Jewish nationalism and anti-Soviet forces in general:
"Dear Joseph Visarionovich!...
"It seems to me that the only radical solution to the Jewish Question in our Socialist State is full assimilation and the merging of individuals of Jewish origin with the peoples among whom they live. I am afraid that a collective statement by a number of people active in Soviet cultural life, united only by their origin, could strengthen nationalistic tendencies. The text of the letter speaks of a 'Jewish people'; this could encourage nationalists and others who have not yet understood that there is no such thing as a Jewish nation.
"I am particularly worried about the influence of such a 'letter to the editor' on the broadening and strengthening of the world movement for peace. Whenever, in various commissions and press conferences, the question has been raised as to why there are no Jewish schools or newspapers in the Soviet Union, I have replied that after the war there no longer remained any breeding-grounds for the former 'Pale of Settlement' and that new generations of Soviet citizens of Jewish descent do not wish to set themselves apart from the peoples among whom they live. The publication of this letter, signed by scientists, writers and composers, who speak of a so-called Soviet Jewish community, could fan repellent anti- Soviet propaganda which is at present being spread by Zionists, Bundists, and other enemies of our Motherland..."
Ehrenburg added that if nevertheless Stalin decided that signing the open letter would be helpful to the cause of the Peace Movement and the Motherland, he would sign it. This sort of self-humiliation (and the posing of ideological [1] and practical objections to the open letter, not moral objections which would obviously have no impact on Stalin) was necessary if the letter was to have any effect.
According to Rubenstein, after Ehrenburg's letter was sent, no more signatures were collected; the organizers of the campaign understood that they could not proceed further until Stalin made some sort of response. He concludes that it is unclear whether Ehrenburg's letter made Stalin reconsider or at least hesitate--and whether this hesitation coupled with Stalin's death, saved the Soviet Jews. In his footnote 60 on page 434 Rubenstein writes that Alexander Yakovlev--the famed "liberal" adviser to Gorbachev, and a man who would not seem to have any motive to whitewash Stalin--concluded, based on research into secret Kremlin archives, that Stalin was not directly behind the plan to exile the country's Jews. Yakovlev believes that Stalin put an end to the scheme before he died, and that Ehrenburg's letter may have played a role. Rubinstein also notes that "Nikita Khrushchev once provided a completely different view of what happened. He claimed that Mikoyan and Molotov objected to the deportation plan and that even Voroshilov said it would be criminal and resemble the acts of Hitler. Khrushchev claimed that Stalin grew furious in the face of their objections and that he suffered his fatal stroke a few days later; see *Le Monde*, April 17, 1956, p. 3." (I think we can dismiss this at least as nonsense, as an attempt by the post-Stalin leadership yo portray themselves as heroes who stood up to Stalin.)
In short, there definitely was an organized campaign to get Soviet Jews to urge their own deportation, and it is difficult to imagine people as prominent as the campaign's organizers proposing such a radical measure unless they were at least led to believe it had Stalin's support. Nevertheless, it is possible it was a "trial balloon" that Stalin would have reconsidered had he lived longer--or that he already had reconsidered before his death in OTL. OTOH, it is perfectly possible he would have gone through with it.
One other possibility which I do not seem to have seen considered (but I admit that apart from Rubenstein I have not read much specifically about this subject): Maybe the "open letter" itself was a provocation, and not those Soviet Jewish "prominents" who refused to sign but those who signed (Vasily Grossman among others) were in the most danger! After all, the open letter claimed that Jews needed to be "protected" from the Soviet people, who apparently could not distinguish between ordinary working people of Jewish origins and the fiendish Zionist doctor-plotters! "Is this not defamation of the Soviet people, comrades? Is this not giving aid to the Zionists and Bundists who slanderously call the Soviet Union anti-Semitic?" Etc., etc.
[1] Note Ehrenburg's emphasis that there is no such thing as a Jewish nation--a point which Stalin had long ago argued in *Marxism and the National Question.* ("Bauer speaks of the Jews as a nation, although they 'have no common language'; but what 'common destiny' and national cohesion is there, for instance, between the Georgian, Daghestanian, Russian and American Jews, who are completely separated from one another, inhabit different territories and speak different languages?")
***
The above was based on something I had written for soc.history.what-if some years ago. More recently, Rubenstein has written a book *The Last Days of Stalin* in which he throws some doubt on the alleged plan:
"In one crucial respect Rubenstein alters our picture of the anti-Jewish campaign. People have long thought that in 1953 Stalin was planning to transfer Soviet Jews to Birobidzhan, the Siberian Jewish “homeland” developed in 1928, just as he had earlier transferred the Chechens, the Crimean Tatars, the Ingush, and other ethnic groups. Scholars have supposed that this massive deportation failed to occur only because Stalin died before he could make it happen. But Rubenstein finds no actual evidence of a plan to transfer the Jews.
"He argues that the anti-Semitic atmosphere was so intense in the months before Stalin’s death that many simply assumed such a project was in the works; the deportation swiftly became a worldwide rumor and within a few years would be reported in the Western press. [Stalin’s successor Nikita] Khrushchev later said that he himself had convinced Stalin not to deport the Jews, but he seems to have invented this story to give himself credit for undoing one of Stalin’s evil plots. . . ."
https://mosaicmagazine.com/picks/2016/06/stalins-last-days-and-his-plans-for-soviet-jews/