McCarthy, 53, is his party's No. 2 House leader and was one of the earliest and steadiest backers of Trump's presidential campaign.
If Trump weighs in to the contest, his clout could rally lawmakers behind his favored candidate, especially conservatives. But it could alienate moderates and others who want a leader who has their back, not necessarily the president's. It's uncertain whether Trump will intervene or for whom, though many suspect it would be McCarthy. White House officials declined comment.
McCarthy was elected in 2006 and rocketed into a leadership job in 2009, thanks to his campaigning for fellow Republicans. He replaced Eric Cantor as majority leader in 2014 after the Virginian unexpectedly lost a primary for his House seat and quit.
In 2015, McCarthy sought to succeed Speaker John Boehner, R-Ohio, who'd alienated conservatives who considered him insufficiently doctrinaire. McCarthy abruptly left that contest days later after failing to line up enough votes, and Ryan accepted the post.
Scalise, 52, the House GOP vote counter and No. 3 leader, was first elected a decade ago and had little national name recognition until tragedy thrust him into headlines. He was shot at a congressional baseball practice last year and is still recovering from his injuries, an ordeal that's earned the conservative former state legislator broad respect.
"The strength he's shown with his injury, I think, has heightened where he is" among colleagues, said Rep. Phil Roe, R-Tenn.
Scalise aides say he and Trump speak frequently, but they provided no detail. Trump visited Scalise in the hospital after his June 2017 shooting. Rep. John Shimkus, R-Ill., Scalise's housemate in Washington, said Trump often calls Scalise out by name at events.
Neither Scalise nor McCarthy have acknowledged a race for Ryan's job or definitively deny it.
"I've never run against Kevin and wouldn't run against Kevin. He and I are good friends," Scalise said Thursday on the Fox News Channel.
That comment put the onus on McCarthy to line up 218 votes, the number needed to become speaker next January should Republicans keep the majority. It was unclear what if any efforts were quietly underway to deny that support to McCarthy, but Scalise's remarks essentially left himself as the alternative.
Lawmakers and GOP donors want a leader who can raise money, and there McCarthy has an advantage. He raised $8.75 million in the first quarter of this year and has done fundraisers for 40 GOP candidates, said a person familiar with his political operation. Scalise has raised $3 million, a record for House whips, and hosted almost 50 events, his aides said.
Neither man is known for rhetorical flourishes, with McCarthy, in particular, prone to sentences that defy the rules of grammar. And both have resume problems that fellow Republicans insisted they'd overcome.
In 2014, Scalise was discovered to have addressed a white supremacist group in 2002 founded by former Ku Klux Klan leader David Duke. Scalise apologized and said he'd been unaware of the group's racial views.
McCarthy suggested in 2015 that a House committee probing the deadly 2012 raid on the U.S. embassy in Benghazi, Libya, had damaged Democratic presidential candidate Hillary Clinton's poll numbers, undermining GOP arguments that the investigation wasn't politically motivated.
That raised questions about his ability as a communicator, a key for party leaders.
Some Republicans prefer Scalise's deep red state background to McCarthy's bright blue California, since the GOP's chief strongholds are in rural and red state districts.
Scalise is viewed as more conservative than McCarthy. That's important in a House GOP conference that could grow more conservative after November, when many Republicans who are retiring or face likely defeat are moderates.
McCarthy has worked to improve his relationship with conservatives, including trying to craft legislation cutting spending from the government budget enacted recently.
Either man could cut a deal with the House Freedom Caucus. Those roughly 30 conservative members theoretically could deliver their votes to a contender in exchange for a promise to back a caucus member for a leadership post.
Associated Press writers Lisa Mascaro and Andrew Taylor contributed to this report.
This story has been updated.