A Republican Massachusetts state representative, Dan Winslow, is considering entering the special election to replace former Sen. John KerryJohn KerryFrustrated Dems say Obama botched Russia response Budowsky: Dems madder than hell Tillerson: 'My view didn’t change' on Paris climate agreement MORE (D-Mass.).

In a statement, Winslow said he was "honored by so many calls and emails urging me to run for the United States Senate," adding that he would consider mounting a run over the weekend, taking into consideration whether the GOP could back a Republican with more socially liberal positions.

In particular, he said he would consider "whether there is room in the national Republican Party for a member who is both fiscally prudent and socially tolerant."

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The search for a Republican challenger for Kerry's seat was thrown wide open Friday, after former Sen. Scott Brown announced he did not intend to run, citing multiple races run in a short period of time and the increasingly partisan makeup of Congress.

Winslow previously served as a U.S. District judge, and also was the chief legal counsel to Mitt Romney from 2002 to 2005 when Romney served as Massachusetts governor. Winslow currently works as a lawyer and a state representative for the Amherst area.

Other possible GOP contenders include local businessman Gabriel Gomez and Richard Tisei, who narrowly lost a House race to Rep. John Tierney (D-Mass.). Neither have officially thrown their hat into the ring.

The Boston Herald reported Saturday that some Massachusetts Republicans are trying to persuade Mitt Romney’s wife, Anne, or oldest son, Tagg, to jump into the race.

Winslow's announcement came as Rep. Ed MarkeyEd MarkeyDems push for more action on power grid cybersecurity Dem senator: Trump 'doesn't respect' the presidency Overnight Regulation: Labor groups fear rollback of Obama worker protection rule | Trump regs czar advances in Senate | New FCC enforcement chief MORE (D-Mass.) geared up his bid to replace Kerry, who vacated his seat after being confirmed as President Obama's new secretary of State.

In an email to supporters, Markey solicited donations for the "short but critical campaign," and warned of possible Republican special interests pouring money into the race.

"While I’ve called on all candidates entering the race to join me and commit to the People’s Pledge that kept special interest spending out of our Senate race last year, we know how badly Karl Rove and his allies want to buy this seat," the email read. "The nation’s focus will be squarely on Massachusetts over the next five months, and we need to be ready."

Markey will face off in a tough primary fight against Rep. Stephen Lynch (D-Mass.), who announced his candidacy for the race Thursday. Markey has already lined up much of the Democratic institutional support for his candidacy, including an endorsement from Kerry himself.

Massachusetts Gov. Deval Patrick (D) recently appointed his former chief of staff, William "Mo" Cowan," to fill Kerry's seat until the special election is held.

--This report was updated at 3:50 p.m.