The Alexandria Dukes, the Washington area's only professional baseball team, may be looking for a new place to hang their scoreboard. A. Eugene Thomas, the Class A ball club's president, says that if the Dukes do not make money this year he will consider moving the team from Alexandria.

An offer of a stadium and a beer license probably would send Thomas on his way.

"I am beginning to run out of patience. I will have to reevaluate the situation for 1983," Thomas said recently when asked if he plans to relocate the team.

"It's foolish for me to continue to struggle when I was not the one to originate the ball club. The city came to me," said Thomas, recalling that former mayor Frank Mann asked him to head the Dukes' citizen-owned corporation when the city acquired the team's franchise in 1977.

"Since then we have not received two nickels. Ten years or five years down the road, Alexandria is going to say, 'What were we thinking of?' " Thomas predicted.

"The Dukes have proven to be the best project Northern Virginia ever had. People are enjoying it and the city is making money."

Thomas said he believes the city has not kept its commitment to the Dukes to build a permanent facility for the team. Mann said the city made no firm promises to build a stadium for the Dukes, however.

City Manager Douglas Harman met with the club's directors several times in the past few years to discuss the possibility of a new location where the Dukes could have their own stadium. Harman said that results of the meetings were negative, however, because of the "fundamental problem of a lack of available land and financing for such a project."

Thomas said that he would wait until the end of this season to decide whether to move the team.

"At that time we will decide what options are open to us," he said. "It is our intention to play in Alexandria." But, he added, "Should an area close to the Washington metropolitan area offer us a facility that would be compatible to AA or AAA classifications AAA baseball ranks just below the major leagues , we would have no problem going to either classification. It's a matter of getting a place to play."

Thomas has said recently that he has talked to representatives of two or three communities in this area that are interested in the Dukes and that the team has received an offer from Frederick, Md., which recently was voted into the Carolina League. Frederick has a 4,000-seat stadium.

"Fairfax County is most interested in bringing back hockey and a higher classification in minor league baseball," Thomas said.

"I don't want to comment," said John F. (Jack) Herrity, chairman of the Fairfax County Board of Supervisors, last week when asked if he and Thomas had been in touch about a possible Dukes move to Fairfax and the upgrading of the team to a AA or a AAA ball club. Herrity noted that if the Dukes did move to Fairfax County, "We would have to rename them."

"We would love to have them, but we will have to see what happens. All I can say is I would have to see then," Herrity said.

Joseph P. Downs, director of the Fairfax County Park Authority, said he knows of no recent discussions between the Dukes and Fairfax County. But he recalled that county officials met with Thomas "about two years ago" to discuss the possibility of relocating the Dukes at a county facility.

"Herrity encouraged Thomas to consider this locality, but we did not have a location that matched up with what he (Thomas) was interested in doing," Downs said. He added that Fairfax County still has no facility that would qualify beyond the Class A level.

Meanwhile, Bill Sullivan, assistant sports information director at George Mason University, said he heard rumors as recently as a month or two ago that the Dukes might be considering a move to Fairfax County. "But I know of nothing specific," Sullivan said.

The Dukes have been operating gypsy-fashion out of vacant classrooms at the Cora Kelly Elementary School in Alexandria--part of the time in a trailer--and playing at Four Mile Run Park for the past five years.

When the Dukes recently rented two additional classrooms, bringing their total to six, the city raised the team's rent by $500, to a total of about $8,000 a month. The rooms were needed for additional office space and to give team's umpire a place to dress, Thomas said. The $8,000 a month, he said, was "just about what it would cost for the team to rent a AAA stadium."

Because of the rent increase, Thomas said, the team probably will not finish in the black this year. Last year, the Dukes made money for the first time in their four-year history, barely breaking even.

"I wish the Dukes well and I would hate to see them leave," said Alexandria Mayor Charles E. Beatley, who occasionally attends Dukes games. "I believe a team is good for the city, but I can't stop Thomas if he feels that he has to have a new stadium. There's no way we could spend three or four million dollars to build them one."

Beatley said that there is a chance that Four Mile Run Park could be upgraded, however. Earlier this year, the city turned down Thomas' request that the city pay for construction of an $80,000 administration building at the site.

"The most the city could do," said Beatley, "would be a shared commitment or something like this. The city would not be willing to make such a commitment unless it had a really viable club with long-term major league commitments guaranteeing the ball club for a substantial period of time."

The lack of adequate facilities does not seem to get in the way of the Dukes' popular manager, former major league infielder John Lipon. "It would be better if we had a nice stadium. The fans would like it better. But we'll play wherever they put us," he said philosophically.