It will be a three-way race after all in the Bay State...

State Treasurer Timothy P. Cahill, who is mounting an independent candidacy for governor, said yesterday that he had rejected entreaties from supporters of Republican rival Charles D. Baker to quit the race and serve as Baker’s running mate.

Cahill said he turned down the proposal, made Friday in a phone call from Joseph Nolan, an NSTAR executive active in Baker’s campaign, to Cahill’s chief of staff. That call, Cahill said, came a few weeks after another Baker supporter, former Weld administration official Mark Robinson, made a more general inquiry to another Cahill aide.

The pairing of the two self-described fiscal conservatives could have posed a strong challenge to Governor Deval Patrick, whose reelection hopes, according to early polls, could rest on a three-way race.

Cahill said that while he was not exactly insulted that Baker, who has never run for statewide office, would ask him to be his lieutenant governor, he was taken aback.

“I feel like I have every bit as much right to run for the top job as he does,’’ Cahill said in an interview. “And I would hope people would respect that.’’

A spokesman for Baker said that no one from the campaign had made a formal offer to Cahill.

“We intend to select a running mate, but it’s an internal process among the candidates, campaign staff, and consultants,’’ said the spokesman, Rob Gray. “Those are the only people who speak for the campaign, on this or any other issue.’’

Nolan could not be reached for comment.

Robinson said the topic came up in an off-handed way at a purely social lunch with a Cahill aide, and he said he had not discussed the matter with Baker beforehand.

But Cahill said it was evident to him that Nolan and Robinson were emissaries from the Baker campaign. He said Nolan even referred to the Baker campaign as we.

“It’s pretty clear they want me out of the race and preferably on Charlie’s team,’’ he said.

UPDATE: Please make sure to turn in Wednesday night at 8:00pm EST for The Notes on Blog Talk Radio. Our guest will be Steven F. Hayward, who will discuss his new book The Age of Reagan: The Conservative Counterrevolution: 1980-1989. Plus, more from Patriot Games Media and the Globe.

SECOND UPDATE: More from Mark Noonan.

THIRD UPDATE: More from the Globe, Don Feder and the Herald.