The National Football League Players Association proposed yesterday that any one of nine private mediators, including four former U.S. secretaries of labor, one of whom is a former Supreme Court justice, be invited to help end its 17-day-old strike against the NFL.

But the NFL Management Council, the league's labor negotiating arm, rejected the proposal, reiterating its call for intervention by the Federal Mediation and Conciliation Service.

"We have problems with a private mediator," said Jim Miller, a management council spokesman. "We haven't resolved one single issue. A private mediator would only inject another issue. We would agree to any one of the 260 mediators with the mediation and conciliation service."

Miller said federal mediators have been keeping informed on the issues in the strike, but that private mediators would have to be educated on such matters and that the process would be time consuming.

Earlier yesterday, Ed Garvey, executive director of the NFLPA, told a breakfast news briefing that federal mediators were not helpful in attempting to resolve disputes with the NFL in 1970 and 1974 and that he is reluctant to invite them in now.

The nine mediators suggested by the NFLPA were former labor secretaries John Dunlop, Ray Marshall, Willard Wirtz and Arthur Goldberg, who is also a former Supreme Court justice; former solicitor general and Watergate special prosecutor Archibald Cox; Theodore St. Antoine, dean of the University of Michigan Law School; the Rev. Theodore Hesburgh, president of Notre Dame; Basil Patterson, former secretary of state for the state of New York, and Arthur Flemming, former chairman of the U.S. Civil Rights Commission and a former secretary of the Department of Health, Education and Welfare.

But, said Garvey, "Until the National Labor Relations Board rules that they (the NFL negotiators) are not following the law, I doubt that a mediator will do much good."

Pending before the NLRB is a union charge that the NFL has been guilty of an unfair labor practice by refusing to bargain on the players' central demand: that a trust fund be established to pay player salaries on a seniority-based scale with performance incentive bonuses.

The NFL has accused the union of failing to bargain in good faith.

In proposing private mediation, Garvey repeated his demand that owners join the bargaining, a demand the management council's executive director, Jack Donlan, rejected Wednesday, noting that a group of owners had met privately with union officials Tuesday.

Donlan also said further talks would be futile as long as the union demands a wage scale, and Miller reaffirmed that position yesterday.

Garvey and Donlan spoke yesterday, and in a message to the union later in the day, Donlan said, "We remain ready to negotiate." However, there was no indication from either side when talks will resume. And the union reaffirmed its commitment to a wage scale.

"We're not going to take it off the table," said NFLPA President Gene Upshaw of the Los Angeles Raiders. "One of the main reasons we are out is because of the wage scale. We feel the strike is just beginning."

In a related development, Dave Dixon, one of the founders of the fledgling United States Football League, said the USFL would not attempt to sign NFL players, even if the NFL calls off its season, if such signings would violate a player's contract with the NFL.