Yes, he did. Molotov visited Berlin from November 12-14 1940 and laid down Stalin's terms for the Soviets joining the Axis. Basically, Stalin wanted influence in Finland, Bulgaria, Romania and the Turkish Straits.
Hitler refused to discuss the subject of Turkey and the Balkans, with the latter claiming he would have to speak with Benito Mussolini on the matter. What he did instead, was issue Directive 18 to the OKW, telling them to continue the preparations for Barbarossa which had begun in June 1940.
While talking with Ribbentrop in an air raid shelter, Molotov basically said the Soviets were 'concerned' about Sweden's neutrality and who would control the exit to the Baltic. Ribbentrop urged Molotov to encourage the USSR's expansion towards India. After Britain was defeated, then Germany and the Soviets could share the spoils by carving up the British Empire.
Basically, Molotov was dragging out the negotiations by consistently trying to establish a Soviet sphere of influence larger than that agreed in the Molotov-Ribbentrop Pact.
A draft agreement was drawn up between the two and was carved up into two halves, one for public release and one for private use only.
The public portion contained an agreement with a ten-year duration whereby the parties would respect each other's natural spheres of interests, while Germany, Italy and Japan would affirm their recognition of existing Soviet borders.
The draft of the secret agreement included the obligation not to join any alliance directed at the four signatories and to assist each other in economic matters. The secret agreement contained a protocol defining the territorial objectives of the four signatories, with Germany laying claims to central Africa, Italy in northern and northeast Africa, Japan in southeast Asia and the Soviet zone to the ”center south of the national territory of the Soviet Union in the direction of the Indian Ocean.
On November 25, Stalin sent a counter-proposal, demanding
Officially, Germany didn't respond. Unofficially, Hitler was frustrated with Stalin's constant demands, calling him a 'cold, blooded blackmailer' and claiming Stalin only sent the offer because a German victory in the war would not be in the USSR's interests. In regards to Molotov's negotiations, Hitler would say...
TL: DR - The Soviet Union joining the Axis would only happen if Hitler was prepared to give up a large swathe of Eastern Europe to Soviet influence, or as John Keegan put it...