Jack Kent Cooke and Washington Mayor Marion Barry have agreed to meet next week to discuss Cooke's desire for a new domed stadium for his Washington Redskins football team.

John White, the mayor's press secretary, confirmed that Barry and Cooke spoke by telephone Friday night, a few hours after Cooke reiterated at the Redskins' Welcome Home luncheon his hope for the District or one of five suburban county governments to "invite us to talk about building a new stadium for the Redskins."

"The mayor has expressed a real commitment for keeping the team here," White said. "He wants to talk to some {other city officials} and wants to meet with Cooke in person before he says a whole lot more publicly."

As mayor, Barry is chairman of the three-member D.C. Armory Board, which oversees the stadium and the armory.

The Redskins' 30-year lease at RFK Stadium, which seats 55,750 for football, will end after the 1990 season. Under its terms, the Redskins pay 10 percent of gross ticket sales as rent during the regular season and 12 percent during the playoffs and share neither in concession nor parking revenues.

The Redskins have a waiting list of 20,000 applicants for season tickets at RFK, which has the third-smallest seating capacity in the 28-team NFL. The Redskins are one of only two teams that do not have luxury suites available for annual rentals, according to the publication Amusement Business. The other team, the Los Angeles Raiders, recently announced that the Los Angeles suburb of Irwindale will build them a stadium with luxury suites.

The luxury suites are attractive to the owners because, unlike regular ticket revenues, receipts from the sky suites are not shared with other teams.

Neither Cooke nor Barry was available for comment yesterday.

In another development, the Prince William County Board of Supervisors voted in executive session Tuesday to write Cooke and request a meeting with him. It represents the first official action by a local county government to pursue the possibility of building a stadium and moving the team to the suburbs.

"The board is hopeful of sitting down and talking to him very soon," said John Gessaman, the county's director of economic development.

A number of suburban officials think privately that Cooke is using them as leverage in his negotiations with the city. But none will say so publicly. As Gessaman put it: "We have to be optimistic about our shot at it. Otherwise, why try?"

He said he would soon begin feasibility studies and said he was uncertain how such a project could be financed. Cooke has given no indications about what kind of financing he is seeking for "Redskins Stadium," as he calls it.

Cooke's meeting with Barry likely will be the first in a long series between the two sides leading to a new lease at RFK if efforts to build a domed stadium do not succeed. "Mr. Cooke made the initial movement by the Redskins," said Jim Dalrymple, general manager of the stadium/armory complex. "He made his feelings known what he would like . . . The mayor knows best what the financial restraints are on the city."