Party officials acknowledge Capito has the best chance to beat Manchin, but the lawmaker is believed to want the governor's job.
Indiana state Senator Mike Delph (R) has been mentioned by Tea Party activists as a favorite to challenge Richard Lugar.
The National Republican Senatorial Committee accused the centrist Democrat of breaking a campaign pledge Saturday.
No candidate has officially announced but George Allen is expected to run and a possible conservative challenger is making waves.
Senate Republicans are $6 million in debt after the election, while Democrats are $6.7 million in debt.
Massachusetts Gov. Deval Patrick (D) ruled himself out of a 2012 challenge to Sen. Scott Brown (R-Mass.), but predicted there won't be any shortage of Democrats in the running.
“If there are as many candidates as have indicated they are interested, there will be a contested primary, and I will stay out of that ... but when it comes to the general election, I expect to be very involved," Patrick said at a luncheon with journalists in Boston on Thursday.
Patrick, who won a second term in November, insisted he won't be one of the candidates in the crowded field.
"I am certainly going to be involved in conversations with would-be candidates and have been already," Patrick said, according to the Boston Herald.
Patrick said he's already talked to "a few" interested candidates but didn't reveal any names.
A state judge in Alaska ruled Thursday that Sen. Lisa Murkowski (R-Alaska) can intervene in the lawsuit initiated by Republican Joe Miller.
Miller is suing the state over the outcome, contesting more than 8,000 write-in ballots his lawyers say were erroneously counted for Murkowski.
The senator was declared the winner in the race earlier this month, but a temporary injunction from a federal judge has prevented state elections officials from certifying the results. Her lead over Miller is more the 10,000 votes.
A judge in Alaska Wednesday agreed that Miller's lawsuit contesting the outcome of the state's Senate contest should be resolved quickly.
Attorneys for the state filed a brief Tuesday, asking a judge to expedite the case over concerns that the state could be without full representation in Congress come January.
Arguments are slated to begin next Wednesday.
Virginia Republican Corey Stewart, who is weighing a bid for Senate in 2012, said Thursday that associates of former Sen. George Allen (R-Va.) are already playing hardball in an attempt to convince him to stay out of the Senate contest.
Allen is widely expected to make another run for his former seat two years from now, but he might face some GOP opposition in the primary.
Stewart, who is the Chairman of the Prince William County Board of Supervisors, is up for reelection in 2011, a race he said those close to Allen have already warned him about.
"They've already started making the threats," said Stewart, who told The Hill that "someone senior in the Allen camp" relayed a message to his office that they intend to solicit interests to pour money into the campaign of Stewart's challenger next year.
"I never back down to a threat," said Stewart. "All that does is make me dig my heels in more."
A senior advisor close to the former senator said simply, "It's not true."
The advisor added that Allen has always had a good relationship with Stewart and while he expects that to continue, he has been "surprised" by some of the chairman's recent public criticisms.
Stewart reiterated that he is seriously considering a Senate bid and will make a final decision sometime next year.
Last week, Stewart said in a TV interview that Allen was a great governor of Virginia, but his record during one term in the Senate was "mediocre."
-Updated at 8:20 p.m.
Attorneys for the state asked a judge to expedite the case over concerns that the state could be without full representation.
Republican strategists expect the party to put its plans for a West Coast expansion on hold after the GOP failed to make gains there in 2010.