Spherical landing craft appear in sci-fi literature as far back as the '50s at least, and while they don't have landing legs per se, the Venera landers for the Soviet space program (landing on Venus) were often spherical in shape. I've no doubt 2001 had an influence, but there's been plenty of similar out there, and a sphere makes a decent pressure vessel, anyway.
As for aerodyne DropShips, Von Braun was proposing similar as far back as the late 1940s, among others, and the early BattleTech devs probably would have been familiar with the Space Shuttle development program.
