Years ago some guy on the forum extrapolated the maximum rating based on draw frequency (the better the players, the more frequently they draw) and got something like 5200 if I recall.
I think it was ozzie_c_cobblepot
That, and of course, ratings are relative not an absolute measure.
How high will engine ratings go? Right now stockfish has a rating of 3400 from the chess.com engine tournament. Is this the max? Will they get to 4000? higher?