All of the US officials and thought leaders in the international politics sphere at that time knew what NATO expansion would mean and knew what concerns USSR/Russia had, and at least publicly took them seriously. I'm not coming with the exact names now, but it was types like Kissinger, Rumsfeld, Mearsheimer, etc. There's even a white paper from one of them, probably during the Clinton administration, discussing how a proposed expansion is playing with fire and should not be considered.
The agreement at the time, which IIRC the West German chancellor confirmed, was that NATO would expand eastward in that the DDR would be taken over by the BRD, but beyond that the alliance would move no closer to Russia.