Control of the Washington Redskin football franchise may change hands bacause a majority of club owners have indicated they favor a policy that bars investments in other professional team sports.

Jack Kent Cooke, majority stockholder of the Redskins, owns the Los Angeles basketball Lakers and the hockey Los Angeles Kings.

Cooke said "no comment" when asked about a report in yesterday's Los Angeles Times that he would divest his interest in the Lakers and Kings and the Forum in Inglewood, Calif., move to Virginia, and stay in football. If he does not sell the Lakers and Kings, he will have to sell control of the Redskins, under the league's divestiture policy.

The Times reported that at least 24 clubs are believed to be in favor of football club owners divesting their interests in other team sports and said a vote to that effect has been taken.

A spokesman for the NFL said no vote has been taken, but he said a majority expressed sentiment in favor of the policy at recent meetings in Palm Springs, Calif., and New York City.

Twenty-one votes would be required to implement the policy, which was placed on the books before the merger with the American Football League in 1966.

The spokesman said "a shopping list" of ideas about the proposal has been sent to the clubs for comment since the last league meeting, in June, and once those comments are reviewed another meeting will be called to consider action.

The spokesman said on such meeting has been scheduled, nor has a time limit been set for divestiture of other sports holdings. He said some club owners were opposed, but he declined to identify which ones.

Three club owners other than Cooke would be affected.

Lamar Hunt, owner of the Kansas City football team, is the majority stockholder in the Dallas soccer team and has a minority interest in the Chicago basketball team. The NFL proposal would not affect Hunt's holdings in tennis.

The wife of Joe Robbie, owner of the Miami Dolphins, is the majority stockholder in the Fort Lauderdale soccer team.

Ed DeBartolo St. is the majority stockholder in the Pittsburgh hockey team. His son owns the San Francisco footballl team.

Elmer J. Nordstrom represents his family's majority ownership in the Seattle football team and has a minority interest in that city's soccer team.

The NFL proposal would apply to families of NFL owners.

The owners likely would elect to keep their NFL franchises because of a new television contract with the three major networks that will provide each club with more than $5 million a year, averged out over the next four seasons.

While a generous time limit likely would be voted to dispose of other sports interests, there probably would be fines imposed to prevent dawdling and the NFL could collect the fines by withholdings payments from television revenue the Time reported.

The Times quoted speculation by unnamed sources that no serious resistance is expected from Cooke or the others because the proposed stepped-up action merely formalizes long-standing policy and beacuse it has been a condition of purchase previously approved by the club owners.

Herman Sarkowsky, managing general partner of the Seattle Seahawks, was approved on condition that he dispose of his investment in the Portland basketball team, which he did.

The Times suggested NFL owners may feel soccer is mushrooming, and that may threaten football and put investors in dual franchises in the position of promoting one sport against the other.

There also was theorizing that NFL owners might incur financial problems in another sport against the other.

There also was theorizing that NFL owners might incur financial problems in another sport that would affect their solvency in football.

Another consideration is that each sport has different regulations, which put the dual owner publicly in a conflict of interest defending those regulations.

As an example, the NFL bars signing a college prospect until his normal class has graduated, but hockey teams sign players in their 20th year of age and baseball and basketball teams sign youths out of high school, the latter in so-called "hardship cases." The National Basketball Association has faced litigation in that area.

Thus, a dual football and basketball owner might find himself defending one league's regulations in court, in principle, while operating in another sport that opposes the principle.

The league spokesman said the key to the one-sport ownership policy is the NFL club owners thing all their "energies, ideas, and resources" should be directed fully to football.