Outgoing Rep. Fred Upton (R-MI) is a name being floated as a potential alternative, per a report from Politico.
The report cites a Republican lawmaker in a bipartisan group looking to find a replacement if McCarthy is unable to get the 218 votes needed.
Upton has served in the House since 1987 but is leaving at the end of this term, meaning if elected as House speaker he would not be a representative. The U.S. Constitution does not mandate that a House Speaker be a member of Congress, but every previous speaker has been.
McCarthy faces a tough battle in trying to win over more conservative members of the Republican conference, who say they will never vote for him. The GOP has won 220 seats in the midterm elections and is ahead in the final two remaining races, per the Associated Press.
With a majority being 218 the GOP can only lose two to four votes from its own party members. McCarthy had 36 members of the conference vote against him in a leadership vote last month.
The House Speaker hopeful has been attempting to win over members of the House Freedom Caucus through various gestures, including providing an extended period of time to debate the House GOP Conference rules and introduce amendments.