By abandoning his fight to be reconfirmed as director of the Office of Personnel Management, Donald J. Devine has opened the possibility of running for statewide office in Maryland after 1986 and solved a ticklish political problem for the state's senior senator, Charles McC. Mathias Jr.

The head of the Republican Party in Maryland and the state's two Republican National Committee members said yesterday that Devine would have little support if he challenged fellow Republican Mathias in the party's primary next year. But those three party officials opened the door to Devine's running for statewide office at a later date, perhaps for the U.S. Senate in 1988.

Rumors of a possible Devine 1986 challenge to Mathias, who held the swing vote on the Senate committee considering Devine's nomination, have circulated for months in Annapolis and political circles elsewhere in Maryland, but the party leadership has all but closed the door to that opportunity. Such a race had been seen as a clash between the party's conservative wing, represented by Devine, and the more liberal faction that identifies with Mathias.

"Eight-six is Mac's year," said Helen Chamberlain, a Baltimore County resident and national committee member. "He's the one who can hang onto that Senate seat for us."

Richard P. Taylor, a national committeeman from Potomac who is a close personal friend and political ally of Devine's, echoed Chamberlain, saying, "Mathias is the incumbent and the party's behind him."

Devine, who was a key figure in President Reagan's campaigns in Maryland in 1976 and 1980, almost certainly is aware of his party's desire for unity in the Senate race next fall. Yesterday, when asked at an impromptu news conference whether he would challenge Mathias next fall, Devine answered by saying, "I have no idea what I will do. I am enjoying being a private citizen."

Devine, a Montgomery County resident, taught political science at the University of Maryland and now does consulting work for the conservative Heritage Foundation in Washington.

By dropping his attempt to regain his post at OPM, Devine erased the prickly question of whether Mathias would have supported him in the Senate Government Affairs Committee's vote on his reconfirmation.

Mathias never announced where he stood on Devine's reconfirmation. Conservative Republicans in Maryland, already angered by Mathias' record on a variety of issues, eagerly awaited the vote to show whether Mathias would part company with the White House, as he had on some past issues.

Instead, Devine's decision to withdraw "takes Mathias off the hot seat and removes any question of antagonism," said Taylor.

Brian J. Berry, the head of the Maryland Young Republicans, said he was disappointed that "Mac Mathias was never put on the record."

"The largest thing that sticks in my craw is that conservative appointees are getting sliced and diced in the Senate veg-o-matic," Berry said. "That's what aggravates us conservatives. And if anyone was one of us, it was Don Devine."

Berry, Chamberlain and state party chief Allan C. Levey said that Devine, who is regarded by many Republicans as an articulate and personable man, could pose a serious challenge in 1988 to U.S. Sen. Paul Sarbanes, a Democrat, who will be up for reelection.

But others said that Devine's efforts to cut the federal payroll while at OPM could work against him in a state where more than 250,000 U.S. government employes live.

"He did exactly what the president wanted him to do, and ran a clean operation at OPM," said Taylor. "But you're not going to play very well with the people you're trying to cut."