The N.F.L. has already promised the coin toss to a former league star, Hugh McElhenny, a spokesman said. It has also arranged to have its own youth choir sing the national anthem at a ceremony in Palo Alto.

Donald Weiss, the executive director of the N.F.L., said he knew of no football rules that would prohibit a flip of the coin taking place a continent away from the stadium.

Mr. Weiss also said the N.F.L. had not been asked about the coin flip. But he acknowledged that he had had discussions with the Inaugural Gala Committee about the national anthem suggestion, an idea attributed by several parties to Mr. Deaver.

'Like the Olympics'

An Inaugural Committee official who declined to be named said the plan was ''to come off the spirit of the thing, like the Olympics.''

''The whole thing, the inauguration and this,'' he said, ''is a happening. It's an ace.''

Last year, more than 100 million Americans watched the Super Bowl, which has often drawn the largest television audience of the year.

The Inaugural Committee official said Mr. Deaver had ''embraced'' the idea of asking the N.F.L. and ABC to include Mr. Reagan in their Super Bowl broadcast.

Several parties also said that Mr. Deaver suggested, through the Inaugural Committee, that ABC, which has the right to broadcast the game this year, televise the game's national anthem from a ceremony in Washington at which President Reagan and Vice President Bush will be present.

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Discussions About Anthem

Mr. Weiss said Robert Janni, a producer of football half-time shows and spectacles who is helping plan the inaugural festivities, had approached him about having the anthem broadcast from Washington.

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''My first contact was with Janni,'' he said, ''and last Friday I had a discussion with Ron Walker, the chairman of the Inaugural Committee.''

Mr. Weiss said Mr. Walker had made it clear that Mr. Deaver was ''very enthusiastic'' about the plan.

''If the President were interested in participating in the coin toss,'' Mr. Weiss added, ''I'm sure we'd be happy to work it out.''

Jim Spence, an excutive vice president of ABC Sports. said: ''There is some interest in having the national anthem from the Jefferson Memorial with the President and Vice President in attendance. The President may also be involved in the coin toss.''

Reagan's Visit to the Memorial

The President is scheduled to visit the Jefferson Memorial to hear the National Youth Choir sing as the first public act of his second term in office. The concert, which is to begin at 5:30 P.M., was suggested to the N.F.L. as an appropriate place from which the Super Bowl national anthem might be broadcast.

The N.F.L. made a commitment months ago that its own 300-voice youth choir would sing the anthem in a ceremony that would also feature 1,200 to 1,400 schoolchildren, who, according to Mr. Weiss, ''will be dressed in white and will form a map of the United States.''

If ''that other matter worked out, the network would be switching back and forth,'' Mr. Weiss said. ''The two groups would be performing a common anthem.''

The N.F.L. had asked to have Mr. McElhenny, who played with the San Francisco 49ers, toss the game coin. In the past, the league has had former football greats like Red Grange toss the coin.

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''But this year,'' said one N.F.L. executive, ''if President Reagan wants to toss the coin, he can toss the coin.''

The Constitution assigns Jan. 20 as the day when the President and Vice President are to begin their new terms of office.

The potential for a conflict with the Super Bowl did not arise until the championship game originated in 1967. Before that, with no Super Bowl conflict on television, Presidents- elect nevertheless postponed their public swearing-in ceremonies to the next day.