Sen. John Warner (R-Va.), a friend of Washington Redskins owner Jack Kent Cooke and a member of the Redskins board of directors, said yesterday that he told Cooke he would research the possibility of federal financing for a new football stadium.

However, Warner said he had concluded that it was "highly improbable" that Congress would approve federal aid for a new stadium, an option that was suggested last week by D.C. Mayor Marion Barry.

Warner said he was "not able to give a judgment at this time" on whether he would support a request for a federal grant, adding, "I may have a conflict of interest."

Warner offered his help to Cooke during a brief conversation Saturday at the annual steeplechase sponsored by the Fairfax Hunt Club, according to both men. "It occurred quite by chance," Cooke said. "I was at the . . . hunt . . . and Senator Warner, astride a beautiful white gelding, or should I say hunter, rode over to me."

"He said, 'Anything I can do that will help this project of yours, please call on me and I'll see what I can do,' " Cooke recalled. "We chatted for a little while and that was the extent of it."

Cooke is seeking a 75,000-seat domed arena to replace Robert F. Kennedy Stadium, which seats 55,000. Cooke says RFK, which is built on federal land, is too small and has hinted that he might move the Redskins to the suburbs if his demands are not met.

Warner said he is sympathetic to Cooke's desire for a new home for the team. "There is no greater unifying force in the nation's capital area than that ball club," Warner said. "I'm quite supportive of his actions to explore options that may be open to improve the . . . facilities of the Washington Redskins."

Warner has served as an unpaid director of the Redskins since 1983. In addition, he and Cooke own neighboring estates in Middleburg, Va. "He's a good friend of mine," Cooke said.

Mayor Barry has said he is committed to keeping the Redskins in Washington. In an interview last week, Barry said a new stadium conceivably could be financed by "a regional cooperative venture" or a one-time grant of federal money.

So far, suburban officials have been less than enthusiastic about helping pay for a new stadium in the District. "We wouldn't pay for one if it was built in Montgomery," said Ed Rovner, special assistant to Montgomery County Executive Sid Kramer.

While pledging to keep the Redskins in the area, Fairfax Board Chairman John F. Herrity has voiced similar doubt about committing public money to a stadium. Herrity and Barry plan to discuss the matter at the mayor's office Friday.

In terms of public funding, that may leave the federal government, which has a long relationship with RFK. The Interior Department owns the land on which the stadium is built. In 1979, after the federal government helped the city pay off the bonds that were used to finance its construction, the Interior Department assumed the title to the stadium. In October 1986, Congress passed a law that transferred the title of the stadium to the District. However, Interior retained title to the land.

Warner said he told Cooke he would "research the law to determine the status of the RFK stadium in terms of the federal interest." Having done so, Warner said, he has concluded that the city would have a hard time getting federal money for a new stadium.