Former Rep. Chris Shays (R-Conn.) told Roll Call he is “very interested” in launching a Senate bid to replace retiring Sen. Joe Lieberman (I).

“We are looking into it very closely,” Shays said Friday, noting that he had some personal issues to work out first.

The interest from Shays, a moderate 10-term Congressman defeated in 2008 by Rep. Jim Himes (D), comes the same day Hartford attorney Brian K. Hill, another Republican, announced his Senate candidacy.

“As a former active duty military officer and JAG attorney, I took an oath of office to defend the constitution of the United States,” Hill said in a written statement. “I am running for the United States Senate because my oath still stands.”

The National Republican Senatorial Committee is not working with Shays or Hill, who is largely unknown in Washington. And Washington Republicans are generally skeptical about their chances in Connecticut, where Democrats have a large voter registration advantage.

Some have been looking to 2010 GOP Senate nominee Linda McMahon to run again, given her immense personal wealth. She spent $50 million from her own pocket on the 2010 race, the most ever spent on an unsuccessful Senate bid.

McMahon has been a visible presence in local politics so far this year, activity many believe signals she will indeed run again in 2012. The former World Wrestling Entertainment chief executive has so far been mum about her intentions, but Connecticut Republicans believe she will make a decision near the end of the month.

Former Comptroller General David Walker is also weighing a Republican bid for the seat.

The conventional wisdom, however, suggests whoever wins the Democratic primary will ultimately win the general election. Rep. Christopher Murphy is facing former Connecticut Secretary of State Susan Bysiewicz in that contest. Roll Call Politics rates the Senate race Leans Democratic.

CQ’s Frank Oliveri contributed to this report.