Cornerback Lemar Parrish has asked the Washington Redskins to trade him because of a personality conflict with Richie Petitbon, the team's defensive coordinator, it has been learned.

"I don't want people to think I'm a troublemaker," said Parrish, a 34-year-old, 12-year veteran who was bothered last season by a bad knee and lost his starting spot to Jeris White. "I am not doing this for spite, but I'm doing what is best for Lemar Parrish.

"I'm a fun guy and it's just not fun playing (for the Redskins) anymore. I'm not taking anything away from the team, the town or Joe Gibbs. He's a hell of a guy and I can play for him. And Bobby Beathard has treated me fairly. But I have a personal problem with someone else that makes it impossible for me to stay. My No. 1 wish is to be traded. I'd rather be somewhere else."

As a result, Parrish has been given permission to make his own deal, subject to the Redskins' approval. Parrish said his new agent, George Campbell, has begun actively pursuing talks with other teams. Richard Bennett, who represents Art Monk and Terry Metcalf, had been handling Parrish's negotiations.

Parrish, an eight-time Pro Bowl participant and one of the league's premier cornerbacks, has told Gibbs he will attend a Redskin minicamp in mid-May but he says he will not report for training camp in July.

"I'd rather not come to training camp," said Parrish, who was obtained, along with Coy Bacon, in a 1978 deal with Cincinnati for a 1979 No. 1 draft choice. "I've made it clear to them that, by then, I should be playing for someone else. Bobby and (I) and my lawyer will have to sit down, maybe at minicamp, and see if we can work out a trade.

"I bought a house in Washington because I hoped it would be the last place I played," said Parrish, who has three years left on his $160,000-per-season contract. "The people have been fantastic, but it's come to a point where I just want to be treated fairly. I don't think I can continue to play under the present situation."

That situation centers on his problems with Petitbon. Although Parrish refused to identify the person with whom he has a conflict, team sources said it was Petitbon, who also coaches the secondary.

Petitbon made the decision to keep Parrish on the bench last year after he had come back from early knee surgery. Parrish missed four games and started eight others, finishing with only one interception, the second-lowest total of his career. He has 46 interceptions in his 12 years, including a high of nine in 1980.

"Lemar came to me and told me that he thought it was time to move on," Petitbon said. "He was upset because I kept using Jeris. But Lemar really never played all that well last year and Jeris didn't play all that badly.

"If he does come back, he'll have to win his job back. His status has changed. He's no longer an automatic. But I have no animosity toward him. If he plays like he did in the past, he'll help us. He doesn't understand that personalities never enter into any decision I make. I only do what is best for the Redskins. He's just at an age where he has to prove he still can play."

The Redskins have dangled Parrish as trade bait the last three years but could never obtain in return what was, in Beathard's opinion, proper compensation. In response to Parrish's trade request, Beathard again has shopped around the veteran cornerback, but gotten no acceptable offers.

"We understand Lemar's wishes, but we won't give him away," said Beathard, who apparently wants at least a fourth- or fifth-round choice in return for Parrish, the oldest player on the Redskins roster.

"Lemar and I had a phone conversation just recently and I explained to him we were having problems moving him because of his age and that he might wind up playing here again. He said he understood that and that he would be able to adjust and do the job like he always has. I think he will play here next year."

Parrish has told Beathard he would like to play for one of three teams: Atlanta, Houston or New Orleans.

Parrish walked out of training camp two years ago and demanded changes in his existing contract, which the Redskins claim were not granted. He returned a week before the first game and had his best season, ending in his selection as an all-pro for the fourth time. Parrish and Beathard say contract problems are not involved now.

The uncertain status of Parrish affects Washington's thinking in Tuesday's draft. The Redskins almost certainly will have to select a cornerback with one of their high picks to avoid being left empty-handed should Parrish be traded.