No chance for this at all. From the US viewpoint the replacement of the Shah by an Islamist government was a pure disaster. From the Soviet viewpoint, while it was obviously less desirable than a Communist Iran and did have potential dangers, it nevertheless also had big advantages (which is not surprising, given that while the Cold War was not a pure zero-sum game, it nevertheless was true that, other things being equal, developments that weakened the US were seen as good by the USSR and vice versa):
"The boon for Moscow was a grave defeat for Washington. The new revolutionary government, deriving its authority from Ayatollah Rouhollah Khomeini, quickly reversed the political-strategic orientation of the former regime, and the process of de-Westernisation began. First, the multinational corporations, especially the American firms, were expelled. Khomeini considered it essential to remove the underpinnings of the Shah's industrialisation programme in order to Islamicise Iran, a step that consequently proved to be a major cause of the country's economic decline. Second, the two American-manned electronic intelligence collection stations—one adjacent to the Soviet border near Bandar Shah on the shores of the Caspian Sea and the other, in Kabkam, a desolate spot in the mountains eighty miles south of Meshed—were shut down. No longer could the United States use them to gather data on Soviet nuclear and missile testing in Soviet Central Asia. (Ironically, their loss was a blow to Soviet hopes of America's ratification of the SALT II treaty, because it strengthened the position of those in the US Senate who opposed the treaty on the ground that effective verification of Soviet compliance had been seriously weakened.) Third, Iran immediately reduced arms purchases and withdrew from the role of policeman for the Persian Gulf, thus depriving the United States of a reliable ally who could safeguard Western interests in the region. Should the Soviet-backed People's Democratic Republic of Yemen (PDRY) attempt to foment another insurrection in the Dhofar province of Oman, Iran would not now send troops to defend the pro-Western Sultan as it had in 1973-75. Nor would it help any of the other Arab monarchs on the Arabian Peninsula, to whom in the long run Khomeini's religious fundamentalism is a far greater threat than the Shah's imperial ambitions ever [had been]."
https://www.jstor.org/stable/2619862
Later on, Iranian-Soviet relations did sour, starting with the invasion of Afghanistan at the end of 1979 and continuing with the 1982-3 crackdown on the Tudeh party. But in 1979, the Soviets still hoped for good relations with Khomeini. They were in fact the first government in the world to recognize the Islamic Republic in February 1979.
https://en.wikipedia.org/wiki/Iran–Russia_relations And there was no likely alternative to the Islamic Republic that would be acceptable to
both the USSR and the US.
(This is not even to mention that the Soviets were historically very reluctant to use the Soviet army abroad for any purpose other than to prop up shaky pro-Soviet communist regimes. Afghanistan was not an exception to this; Iran would have been.)
