The list of potential challengers includes Gov. Jon Huntsman Jr.'s chief of staff, Jason Chaffetz; state Rep. LaVar Christensen of Draper, and Salt Lake County Sheriff Aaron Kennard. KSL radio talk show host Doug Wright also isn't ruling out a bid.
Matheson serves in a majority Republican district but won his most recent election by a nearly 12 percent margin. Republicans, though, still consider Matheson vulnerable, said the National Republican Congressional Committee.
"The race is absolutely on the radar," spokesman Ed Petru said Friday. "At this point, there are a lot of capable candidates looking at the race."
Wright's name is even floating among some Republicans in Washington, D.C. Wright said in a telephone interview he's "flattered" by those comments and admits he has had a "few casual conversations" about running. But, without ruling out a bid, he adds, "I'm not a candidate."
Chaffetz says it's still "premature" to say he's in the race, but "I am seriously considering it."
He says the decision could be made in the next few weeks and he is still talking to the governor about how the logistics of running for office would work with his current job. Chaffetz says he understands he may have to take a leave of absence or leave his job if he enters the race.
As for why he would run, Chaffetz says, "We can do more for the state by electing a Republican."
State Republican Party Chairman Joe Cannon says he has heard from Chaffetz, Kennard and Christensen about possible bids. "There's sort of an intensity around the three of them," Cannon said.
Kennard and Christensen did not return calls seeking comment.
Matheson's spokeswoman, Alyson Heyrend, says they never thought he would be unopposed in the next race.
"It really doesn't matter to Congressman Matheson who his opponent is," Heyrend said. "His approach is to be the best congressman he can for the state."
According to his last financial disclosure, Matheson has about $333,000 cash on hand in his war chest.