PORTLAND — Gov. Paul LePage has floated the idea he could play a role in a Donald Trump presidency, a move that might benefit the state’s Senate president, a fellow Republican with whom he has had a tepid relationship.

LePage, whose term as governor doesn’t expire until 2018, would have to leave office early if he served with Trump. The state constitution says that would mean the Senate president would then become governor.

The president of the Senate is Michael Thibodeau, who has shown more willingness to work with Democrats than LePage has. Thibodeau, of Winterport, also has taken LePage to task in the past, including during 2015 budget negotiations, when he said LePage’s repeated criticism of the process “overshadowed much of the good in the budget.”

Thibodeau and LePage also clashed last year when the governor wanted Government Oversight Committee co-chairman Sen. Roger Katz, also a Republican, to recuse himself from an investigation involving the governor. Thibodeau stood up for Katz.

Thibodeau said this week that he isn’t thinking about the possibility of becoming governor. He said he’s concentrating on his own re-election drive, against Democrat Jonathan Fulford, and making sure the Republicans retain control of the Senate.

“I’m not sure whether he’s serious about wanting to pursue a position in the Trump administration,” Thibodeau said, adding that “the governor and I agree more than we disagree.”

LePage’s staff did not respond to a request for comment Thursday. LePage has said in recent town hall meetings he’s considering running against U.S. Sen. Angus King, an Independent, in 2018 if he’s not a member of Trump’s administration.

LePage has been elected to serve as one of the delegates to this year’s Republican National Convention in Cleveland. He described Trump, the party’s presumptive presidential nominee, as a “true blue American” during Maine’s Republican caucus in March. He has described himself as “Donald Trump before Donald Trump became popular,” a reference to the blunt style favored by both men.

State Democrats aren’t too caught up in the possibility of LePage going to Washington, D.C., said Rep. Drew Gattine, of Westbrook.

“Right now Paul LePage is the governor, he’s the person we have to deal with, as difficult as that may be at times,” he said. “I don’t spend a whole lot of time thinking about those comments even when the governor makes them.”

The state last promoted a Senate president to governor in 1959, when Clinton Clauson died in office and John H. Reed became governor. Clauson was a Democrat who served for a little less than a year; Reed was a Republican who served for more than seven years.

Editor’s clarification: In order for the above scenario to play out, Senate President Michael Thibodeau would have to be reelected to office in November and then reelected by his peers as president of a Republican-held Senate.