Stevens was convicted last month of seven felony corruption charges. His Senate colleagues say they would rather not have to expel Stevens if it looks likely he will lose his race against Anchorage's Democratic Mayor Mark Begich, who leads in the Alaska recount.
Politico reported Monday if Stevens wins re-election but is expelled from the Republican caucus, he will lose his committee assignments and his ability to vote on party matters.
Sen. Jim DeMint, R-S.C., has said he will ask Senate Republicans at a 9:30 meeting Tuesday morning to vote on expelling Stevens from the Republican Conference.
"Senator DeMint can raise it, but members might not be in any mood, especially since the election won't be settled by then," said one Senate Republican leadership aide. "I just don't know what will happen."