Senate Majority Leader Thomas K. Norment, Jr. (R-James City) gestures during a floor speech in August. (Bob Brown/AP)

A leadership fight could be brewing among Republicans in the Virginia Senate.

Sen. Thomas A. Garrett Jr. (R-Louisa) said on a radio program Monday that he does not want Sen. Thomas K. Norment Jr. (R-James City) to continue serving as Senate majority leader. Garrett said he was opposed because Norment also is in line to become chairman of the powerful Senate Finance Committee, whose current co-chairs are retiring.

“I’m in the anybody-but-Senator-Norment-to-lead-the-Republican-caucus camp right now,” Garrett said on “The John Fredericks Show.” “I do hope there will be a leadership change. There are a lot of machinations right now.”

Norment did not immediately respond to messages seeking comment.

Senate Republicans retained their slim 21-19 majority in elections last week. They will vote on caucus leadership next week.

“Every senator has a vote, and every vote will be counted,” said Jeff Ryer, spokesman for the Republican caucus.

Norment has been a member of the Senate since 1992 and the chamber’s GOP leader since 2008, when the party was in the minority. Norment came in at a time when Senate Republicans tended to be more moderate, but he has moved rightward along with the caucus over the years.

This spring, he acknowledged having an affair with a lobbyist whose firm regularly pushed for legislation that Norment voted for and, in two cases, sponsored directly. He said at the time that he had not given her bills special treatment. Federal investigators reviewed the relationship, closing the matter without criminal charges.

There have been rumblings for some time that Norment could face a challenge from within his caucus over ideology or ethics. But Garrett voiced concern only about making one person majority leader and finance chairman. Norment also is in line to become Senate pro tempore, but that is a largely ceremonial role given to the senator with the longest tenure.

“No one person needs that much power,” Garrett said in an interview with The Washington Post. “It’s happened before, and it’s never ended well.”