Undisputed heavyweight champion Mike Tyson finally will fight Michael Spinks in June, barring any more arguments between promoters, managers and attorneys, representatives of each fighter said yesterday. The long-awaited bout of undefeateds has been orally agreed on and contracts should be signed next week.

The date will be sometime between June 10 and June 24, and four sites are bidding: Caesars Palace (Las Vegas), the Las Vegas Hilton, Atlantic City and Madison Square Garden (New York City). Bidding already has reached a record $8 million.

The much anticipated bout between Tyson, the 21-year-old champion, and Spinks, currently untitled but considered the only true challenger, at one point appeared doomed by personality conflicts and financial arguments. But talks began anew over the last two weeks through mediator Shelly Finkel to stage what is already being called the richest fight in history, and he told the Baltimore Sun yesterday "it looks very good at this point."

"The fight was dead, but we all felt it would be the best thing for both fighters to get it on somehow," said Finkel, who served as a go-between for Tyson's comanagers, Jimmy Jacobs and Dave Cayton, and Spinks' manager Butch Lewis.

Sources said Spinks, 31, who calls himself "the people's champion," has been guaranteed between $13.5 and $14 million for the bout. Tyson will receive everything else from the closed circuit revenue and gate receipts, and could wind up in the $17-to-$20 million range after promoter Don King is paid.

Finkel, who also owns the closed circuit and pay-per-view rights to the bout, estimated the production could net a profit approaching $40 million. However, prefight speculation can be exaggerated.

Lewis said the contracts should be signed by next Thursday. The major snag in previous negotiations came when Lewis walked out of a session on Jan. 23, the day after Tyson knocked out Larry Holmes in Atlantic City. Cayton and Jacobs had then refused to deal with him personally, which led to the entrance of Finkel, the prominent manager-promoter and friend of Jacobs and Cayton.

"We came to a verbal agreement on the deal and the lawyers are reducing it to writing," Lewis said. "We'll make sure the i's are dotted and the t's are crossed, and then we'll go on to signing.

"In negotiations with $50 and $60 million, it's not easy. But it's something I think we just had to pursue until we were able to put aside the egos. We said, 'Let's sit down and do business because this is the best thing for both fighters.' It's the only fight."

The job of Finkel, who helped promote the Sugar Ray Leonard-Thomas Hearns welterweight championship in Las Vegas, was made easier by the fact that both sides were eager to stage the bout of undefeated heavyweights.

"It was cordial," Finkel said. "I think it's a good deal for both parties. No one got shortchanged. It will definitely be the biggest fight in history."

Cayton predicted after Tyson's knockout of Holmes that his fighter could earn $50 million in the next year. But none of Tyson's tentatively scheduled bouts had the interest and potential of a meeting with Spinks.

A former International Boxing Federation heavyweight champion, who twice defeated Holmes, Spinks was stripped of his title when he dropped out of the HBO unification tournament in order to fight Gerry Cooney last year. But Spinks is widely considered the only boxer with a realistic chance of defeating Tyson, who went on to unify the title by defeating Tony Tucker, the short-time IBF champion largely by virtue of Spinks' default.

Tyson's next bout is March 20 against Tony Tubbs in Tokyo. He recently signed a new seven-fight, $29 million deal with HBO extending into 1989. It has a clause allowing Tyson to fight Spinks on closed circuit.

The richest fight to date was Leonard's WBC middleweight championship defeat of Marvin Hagler at Caesars Palace last May. The purse exceeded $23 million with Hagler guaranteed $11.5 million while Leonard made roughly $12 million.

Once the contracts are signed, the next set of intriguing negotiations will be those to determine the location. Sources said a bidding war unofficially has begun, with Caesars Palace initially offering $8 million, but that apparently has been surpassed and offers could reach the $9 million range. In comparison, Caesars paid a then-record $6.7 million for Leonard-Hagler.

Real estate magnate and Atlantic City casino owner Donald Trump has allied himself with King and succeeded in giving the Las Vegas Hilton and Caesars Palace unwanted competition for some recent bouts, including the Tyson-Holmes show, headquartered at Trump Plaza and fought at Convention Hall.

"Bigger than huge is what it is," said Trump Plaza vice president Mark Etess, who is trying to obtain this fight also for the convention center adjacent to the hotel.

The entrance of Madison Square Garden into negotiations raises the romantic possibility of the first major heavyweight fight there since Muhammad Ali fought Joe Frazier in 1971.

"No other fight makes sense," Lewis said.