Gov. Paul LePage’s displeasure with Senate President Mike Thibodeau could escalate from the governor’s repeated public criticism of a longtime conservative ally to a challenge in next year’s Republican primary.

Thibodeau, of Winterport, said he has heard that former state Sen. Carol Weston is preparing to run against him in June. Weston said she “absolutely has no plans to run,” but declined to rule it out. Speculation has swirled about her candidacy among Republican activists and lawmakers. If she runs, a widely publicized rift between the governor and Republican legislators will take center stage in the Senate District 11 contest.

A primary contest between Thibodeau and Weston or another candidate would have ramifications for the direction of the Maine Republican Party, which has been torn by divisions between LePage loyalists and other lawmakers who disagree with him. A primary battle would also create distinct parallels between Maine and Kansas, where Republican Gov. Sam Brownback successfully purged legislators from his own party in 2012 after they opposed his efforts to slash the state’s income tax.

Thibodeau, who opposed LePage’s controversial tax overhaul this year, said he was focused on the upcoming legislative session and recruiting Republican Senate candidates to run in 2016.

“I have heard the rumors,” Thibodeau said. “The simple fact is that anybody has a right to run for the nomination. I plan to run. The people of Waldo County can decide if they want me to continue to serve them.”

Weston repeatedly said that she isn’t planning a primary challenge. However, she also reiterated that Republican lawmakers who don’t “support lower taxes and educational freedom for families and smaller government” should be challenged. Asked whether Thibodeau has met those requirements, Weston wouldn’t answer directly.

“That’s for someone to decide,” she said. “That’s the litmus test that I think is best for Maine people, to have choice, lower taxes and the lowest government intervention. That’s what I hope the voters will look for.”

Asked whether she could rule out a run for the Senate next year, Weston said: “I absolutely have no plans. But I’ve been in this long enough to say never say never.”

Thibodeau has repeatedly declined to address speculation that the governor has been trying to recruit a candidate to take him on next year.

“I don’t know if it is his plan to recruit (a challenger). You’ll have to ask him, not me,” he said.

Brent Littlefield, political adviser to LePage, didn’t respond to a request for comment Sunday.

Rep. Jeff Timberlake, R-Turner, said he asked the governor last week if he was trying to persuade Weston to run.

“He told me, ‘I haven’t encouraged anybody to do anything,’ ” Timberlake said. “I had heard a lot of talk about it, so I asked him. There’s a lot of talk about everything up there.”

Weston’s intentions are unlikely to materialize until after Jan. 1, when candidates for the Legislature can take out nomination papers with the Secretary of State’s Office.

The Montville Republican preceded Thibodeau, serving four terms in a seat formerly known as District 32. Republicans have had success in the district despite having only a slight edge in registered Republican voters over Democrats. The district is composed of rural and conservative towns like Waldo and coastal areas like Belfast that lean progressive.

Thibodeau was first elected to the seat in 2010, after he and other Republican activists successfully led a people’s veto campaign to overturn a sweeping tax overhaul passed by the Democrat-controlled Legislature in 2009. Thibodeau’s opposition to the tax overhaul influenced his resistance to the governor’s tax initiative this year. While the governor’s plan differed in many ways from the 2009 initiative, it was similar in concept, dramatically lowering the state’s income tax and partially paying for it with a significant sales tax increase and broadening it to include currently exempt goods and services.

Republican opposition to the governor’s tax plan prompted LePage to declare in March at a Maine Heritage Policy Center event in Bangor that he’ll run against any legislator who opposes his plan, regardless of party affiliation. His criticism of Republican legislators, and Thibodeau in particular, has increased ever since – despite the Senate president’s conservatism and record of support for LePage.

In June, after Thibodeau and Democratic House Speaker Mark Eves reached a tentative budget deal that jettisoned the governor’s tax plan, LePage’s political machine, led by the governor’s daughter, Lauren LePage, initiated a series of robocalls against the Republican Senate leader and others. The 90-second telephone messages accused Thibodeau and other Republican senators of conspiring with liberal Democrats.

During a June 4 interview on WGAN radio, LePage denied responsibility or knowledge of the calls. He also said he didn’t regret that it happened and indicated that the targeted senators owed their 2014 electoral wins to his popularity.

“I will say this: I helped a lot of people in the Senate get elected,” LePage said. “I will just say that. My coattails were pretty well stomped on.”

Thibodeau narrowly won his re-election bid in 2014, beating Democratic challenger Jonathan Fulford by 135 votes.

Weston directs the Maine chapter of Americans for Prosperity, a national nonprofit funded by billionaire industrialists Charles and David Koch that has become a force in national and state elections. The group played a significant role in the defeat of Republican state legislators in Kansas during the 2012 primaries, with backing from Brownback, the governor.

It’s unclear whether a Weston candidacy against Thibodeau would receive the same financial or activist backing. The Republican Senate president is known as a fierce campaigner whose rise in the Legislature was fueled by his success in recruiting and getting Republican candidates elected.

Thibodeau isn’t the only state lawmaker estranged from the governor, who has used a series of town hall meetings across the state to sharply critique Republican and Democratic lawmakers. He has said one-third of Maine legislators are “rubber stamps” for party leaders, and another one-third are in politics for selfish reasons.