Massachusetts Republicans are still searching for a high-profile candidate to run in the special election to replace John Kerry in the U.S. Senate, with former Gov. William Weld the latest to say he is not interested.

The GOP scramble began Friday when former U.S. Sen. Scott Brown announced that he would not be running in the June 25 election.

Weld served as governor from 1991-1997 and ran unsuccessfully for the Senate against Kerry in 1996. He later moved to New York, but recently returned to Massachusetts to join the law firm of Mintz Levin.

"While I am grateful for the kind expressions of support and encouragement which I have received, I will not be a candidate for United States Senator from Massachusetts in the special election this year," Weld said in a brief statement released by the law firm Monday.

Richard Tisei, the former Republican leader of the state Senate, released a statement over the weekend saying that he would not be a candidate. Tisei ran for the U.S. House last year, narrowly losing to veteran Democratic Rep. John Tierney.

Monday evening, Kerry Healey, who served as Mitt Romney's lieutenant governor, also opted against a run, as did Romney's son, Tagg Romney.

State Rep. Daniel Winslow, a Republican from Norfolk, said he would make an announcement on Tuesday whether he would seek the seat. Winslow is a former judge and served as chief legal counsel during the Romney administration.

Gabriel Gomez, a former Navy Seal, has expressed interest in running as well. If more than one Republican gets into the race, they would square off in a primary on April 30.

U.S. Reps. Edward Markey and Stephen Lynch are seeking the Democratic nomination to run in the special election to succeed Kerry, who resigned from the Senate last week after 28 years to become the new U.S. secretary of state.

Middlesex County District Attorney Gerard Leone said Monday he won't run in the Democratic primary.

The clock is ticking for prospective candidates, who have until Feb. 27 to collect 10,000 signatures from registered voters if they wish to run in the Democratic or Republican primaries.

Gov. Deval Patrick appointed Mo Cowan, his former chief of staff, to serve as interim senator until the special election is held.

With additional reporting by the WBUR Newsroom