Irsay said at the NFL owners' meetings Tuesday he wouldn't vote to approve the radio talk show host.
Several players have said they wouldn't want to play for the conservative commentator. Limbaugh was forced to resign from ESPN's Sunday night football in 2003 after making comments the league felt were racially insensitive.
NFL commissioner Roger Goodell said the league doesn't want its owners making divisive statements. But Goodell said he wouldn't judge Limbaugh's prospective ownership because the current Rams owners haven't even said for sure they will sell the team.