AIUI this is the kind of thing that Congress could do, but Baker (the US Secretary of State) could not.

Standard negotiations really — a minister or another member of the executive negotiates with someone and eventually takes a text to a parliament, and in the end that parliament either ratifies the text or doesn't. There's no promise until the relevant parliaments have promised, because the executive does not have that power. The legislature has that power.

Some others did reach out and ask them directly. Gorbachev, his minister of foreign affairs, and his minister of defense all publicly refuted it. It would have been a major commitment, yet there is no trace of it having been discussed internally in Moscow or with other Warsaw Pact countries. Furthermore, according to the USSR's foreign minister at the time, the speculation of such assurance is anachronistic, because the Soviet leadership did not expect the Warsaw Pact to dissolve and therefore had no reason to discuss anything like this.