Tagg Romney (left) with parents Mitt and Ann Romney after the New Hampshire Republican presidential primary. (Melina Mara/The Washington Post)

Former Massachusetts governor Bill Weld (R) will not run in this year's special election for the Senate seat vacated by Sen. John Kerry (D-Mass.), the Associated Press reports. Meanwhile Tagg Romney, the eldest son of former Massachusetts governor Mitt Romney, is considering a bid.

Republicans are searching for a candidate for the June 25 election now that former senator Scott Brown has announced that he will not run. Democrats have rallied around Rep. Ed Markey, although he faces a primary challenge from Rep. Stephen Lynch.

Josh Romney told the Post that he hasn't talked to his brother about the race and doesn't know of any plans. Romney allies insist that the oldest son of the 2012 presidential nominee had given little thought to a run for political office prior to Brown's decision not to run. Romney, while intrigued by the race, has six children -- three of whom are under the age of two -- and a prospering business that would need to be put on hold to run. One source close to the family says Romney is not likely to run.

Other potential candidates include former Lt. Gov. Kerry Healey and businessman and former Navy SEAL Gabriel Gomez, whom national Republicans have been recruiting. Former state Sen. Richard Tisei, who ran unsuccessfully for Congress last fall against Rep. John Tierney (D), will not compete for the seat.

Gov. Deval Patrick (D) appointed his former chief of staff, Mo Cowan, as a placeholder until the new election.

Weld, who served as governor from 1991 to 1997, lost a competitive race with Kerry in 1996. He also ran unsuccessfully for governor of New York in 2006.