Bisping (23-4) is scheduled to fight Belfort at a UFC on FX event on Jan. 19 in Sao Paulo, Brazil.
"In that division, there were so many guys coming up," White told ESPN.com. "A couple of those guys lost tonight.
"If Bisping can beat Belfort -- that's a tough fight for Mike -- he deserves the shot at Anderson."
The same does not hold true, apparently, for Belfort (21-10), who came up short in a light heavyweight title fight against Jon Jones in September.
Belfort challenged Silva for the 185-belt in February 2011 and lost via first-round knockout.
"That fight was so decisive, it would be tough to throw Vitor back in there," White said. "Anderson is going to want to fight new guys. New challenges.
White still maintains Silva (33-4), the most dominant champion in UFC history, will fight welterweight champion Georges St. Pierre and light heavyweight champion Jones before he retires.