Jack Kent Cooke has written D.C. Mayor Sharon Pratt Dixon concerning his efforts to build a new football stadium for his Washington Redskins, and Dixon evidently is trying to arrange a meeting with Cooke.

"Mr. Cooke sent a letter to the mayor suggesting a meeting, and she is in complete agreement," Dixon's sports liaison Henry A. Hubschman said yesterday. "She was planning to do that anyway. . . . The feeling now is that we want to get moving on this thing."

The Redskins' lease for RFK Stadium expired with the end of their season Jan. 5, and while it seems clear the team will back there next season, a lease extension has not been concluded.

"I hope to meet with {Dixon} soon," Cooke said. "She is faced with tremendous takeover problems, and one must be patient."

Hubschman and D.C. Armory Board General Counsel Artis Hampshire-Cowan said Dixon is anxious for an agreement with Cooke that will keep the Redskins in the District.

"Mayor Dixon has indicated that she plans to do whatever is reasonable to keep the Redskins here," Hampshire-Cowan said. "She would like to reach an agreement quickly."

To help facilitate that, Hubschman said Dixon plans to propose to the D.C. Council that she replace Marion Barry on the three-person Armory Board. Although Barry is no longer mayor, he is still serving on the board. An incumbent mayor does not automatically become a member of the board, but Barry nominated himself and has not officially been replaced. The board's other members are businessman Stuart Long and Maj. Gen. Calvin Franklin of the D.C. National Guard.

However, Councilman Frank Smith (D-Ward 1) plans to reintroduce legislation that would make the Armory Board part of a D.C. Sports Authority, one of Smith's staff members said. The D.C. Boxing and Wrestling and D.C. Baseball commissions also would be consolidated into the Sports Authority, which would be responsible for promoting the District as a site for major sporting events and baseball expansion.

Hubschman said Dixon has met with Councilman William Lightfoot (D-At Large), who has replaced Smith as chairman of the Council's Public Services Committee. That panel has oversight over the Armory Board.