The world's top men's tennis players have been offered under-the-table appearance fees of upward of $125,000 each by at least seven tournaments on the Grand Prix circuit, according to a highly placed tennis source.

The source told The Washington Post that to insure getting Bjorn Borg, John McEnroe and Ivan Lendl, each of the seven tournaments has agreed to guarantee each player $125,000, in addition to the regular prize monies. Jimmy Connors and Vitas Gerulaitis have been offered approximately $100,000 each per tournament.

Such appearance fees would enable the players to be very selective about which tournaments they enter in 1982.

Grand Prix rules prohibit such fees for appearances, as well as guarantees against prize money. The rules do not prohibit pay for endorsements by players.

There are 88 tournaments on the Grand Prix circuit.

One tournament official, John Harris, cochairman of the D.C. National Bank Tennis Classic, formerly the Washington Star International, said the practice of appearance fees is "widespread" in Europe, and that there are some players who ask for guarantees. Harris would not name the players. He said no appearance fees ever have been paid, or sought, in Washington.

According to Harris, one tournament in Europe gives a free automobile, worth about $50,000, to each top player, who in turn can sell the car within two weeks.

"It's a real problem," Harris said of the practice of guarantees.

Marshall Happer, administrator of the Men's International Professional Tennis Council (MIPTC), said, "A lot of people do not understand what is or isn't a guarantee, but any time we get information that suggests guarantees, we do an investigation. The questions we ask are, was it (fees or guarantees) a condition of (the player's) entry, and is it for value received?"

Happer said his office had begun an investigation last week into a tournament that may have violated the guarantee code. According to the MIPTC, the tournament and player can be fined for violations, and the tournament can be dropped from the Grand Prix circuit.

"To be fair, we rewrote the code for 1982 and it has a lot more teeth in it," said Happer.

He added, "We do not have rules against players making money, by making store appearances, for example, or playing in a pro-am. But the guarantee rule is to prohibit payment for them just to appear. We want tennis players playing for prize money, not guarantees."

None of the players in question was available for comment the past two days.

Borg, who recently returned from a five-month layoff from tennis, has said he will play only seven tournaments this year instead of the 10 required by the MIPTC.

When Borg failed to comply with that regulation, MIPTC ruled he would have to qualify for every tournament he entered. Borg said he would play neither the French Open nor Wimbledon if he had to qualify. He has won Wimbledon five times.

But Borg does plan to play tournaments in Hamburg, Cincinnati, Tokyo, London and Toronto (the Canadian Open). He recently played in Monte Carlo and Las Vegas. Spokespersons for the Alan King Open in Las Vegas and the Canadian Open said yesterday their tournaments have made no guarantees to Borg. Officials of the other tournaments Borg has entered could not be reached for comment.

Bob Kain, who represents Borg, Connors and Gerulaitis, said, "Are those the only players you've ever heard those rumors about? I've heard things about every player, and I think it's because people lump together endorsements and promotional fees. How do you separate the two? My job is to line up commercials and endorsements. There's no one who's not doing that (endorsements)."

One of Borg's commercial affiliations is with Caesars Palace, for which he has served as touring pro since 1979, and for which he does promotional work during tournaments there. Borg lost in a qualifying match there last week to Dick Stockton.

"Every player is playing for prize money," Kain continued. "The big guys are playing for prize money and computer points, rankings. They make so damned much money playing tournaments and exhibitions, they don't have to think about money. They're interested in rankings.

"And if they play for prize money and points, whatever they do other than that isn't anybody else's damned business."

Jerry Solomon, who represents Lendl, said the concept of "appearance fees" is sometimes misinterpreted. "If a player has an agreement with a company to do a certain number of appearances in a year, and if some of those appearances happen to fall during the week of a tournament sponsored by that company, does that mean the player is receiving an appearance fee, which is against Grand Prix rules, or is it a legitimate fee (from the company)?"

Solomon, who said Lendl would not accept appearance money, said the fact that the Association of Tennis Professionals and MIPTC have not been able to come up with a clear definition of what constitutes a guarantee or a legal fee has made this "a very gray area" of discussion.

"It's a problem as to how the rule can be stated," he said.

John McEnroe Sr., who represents his son, said the junior McEnroe does not accept appearance fees. "I have heard people say players take appearance fees, but with respect to John McEnroe, I know that's inaccurate. I haven't heard anything specific about anybody, but John McEnroe does not accept fees for appearances (in Grand Prix events)."

When questioned about the alleged appearance fees on the Grand Prix circuit, MIPTC administrator Happer said misunderstandings stem from players' numerous endorsement affiliations. "If a guy represents a line of clothing made in Italy, for instance, he has to wear those clothes world-wide, and has to play in a certain number of tournaments in that country. It's an incidental part of it.

"But when he plays there, people say he's getting paid just to be in the tournament, and it's just not true."

Happer said he is concerned about alleged appearance fees because "if we have players paid to play, are we going to be like pro wrestling? When you find out about it (payment to play), it's too late, you've lost it. And if you lose your integrity, you lose everything in tennis."

In 1977, CBS-TV, some tennis players and promoter Bill Riordan of Salisbury, Md., were criticized for advertising that three of the four so-called "Heavyweight Championship of Tennis Challenges" were winner-take-all when, in fact, there were preset financial guarantees regardless of the outcome. These matches involved Jimmy Connors against John Newcombe, Manuel Orantes and Ilie Nastase.