DAYTONA BEACH, Fla. — NASCAR teams have hired one of the country’s top antitrust and sports lawyers to advise them in their ongoing dispute with the family-owned stock car series over a new revenue-sharing model.

The decision to hire Jeffrey Kessler, partner and co-executive chair of Winston & Strawn LLP, followed a Saturday meeting at Daytona International Speedway that included the majority owner from each of the 15 chartered teams in NASCAR. Although the teams invited NASCAR representatives to attend, none did.

Kessler’s hiring was revealed to The Associated Press on Sunday, the eve of the rain-postponed Daytona 500, by the five members of the team ownership negotiating committee. It comes amid a breakdown in negotiations between teams and NASCAR that led the 36 chartered teams to decline last month to extend their exclusive negotiating window with the sanctioning body on the existing deal.

The current charter agreement expires at the end of this season, and two years of talks were stalled by NASCAR’s ongoing negotiations on a new $7.7 billion television rights deal announced in early December. NASCAR’s economic offer to the teams came shortly after but with zero room for the teams to counter.

“We want to make a deal, we are just looking for a fair deal,” Curtis Polk, a part owner of 23XI Racing and member of the teams’ negotiating committee, told The Associated Press. “There is no give-and-take. We’ve been told, ‘This is all there is; there is no flexibility.’ That’s not a negotiation.”

Kessler has been retained so far only to help advise the teams in their negotiations. Kessler most recently successfully represented Division I college football and basketball players in a landmark antitrust case that led to financial stipends for athletes. He also led the U.S. women’s national soccer team in its successful fight for equal pay as well as litigations for current free agency rules in the NBA and the NFL.

The issues between NASCAR and the race teams are far beyond revenue and charters, which are essentially a version of the franchise model used in nearly all professional sports. The teams have asked for the charters to become permanent, which NASCAR has not even considered.

But after a Saturday meeting that included NASCAR’s winningest owner, Rick Hendrick, who is launching his 40th-anniversary season, as well as Roger Penske, Joe Gibbs, Michael Jordan and others, it became clear that having a franchise to leave as part of their legacy remains one of the more pressing topics.

The negotiating team said it couldn’t even come to a resolution in which charters would last seven years but could be revocable by NASCAR based on failing to meet competitive standards. NASCAR has apparently stopped negotiating with the committee and is instead trying to speak to teams individually.

“This whole thing is such a monopoly that you kind of get shut down in different areas, you’re allowed in some place but not in others,” said three-time Daytona 500 winner Denny Hamlin, owner of 23XI Racing with Jordan and Polk.

Each of the 15 teams made the decision on their own to not extend the exclusive negotiating window with NASCAR; the committee told AP that although NASCAR chairman Jim France occasionally meets individually with the teams, he has not been part of any wider meetings as a representative of the sanctioning body.

It has left the five-member executive board representing the race teams entering negotiating meetings with the ability to reach an agreement on behalf of the chartered race teams; the negotiating committee believes France’s absence from the meetings undermines what could actually get accomplished during the session.

But also, beyond the economics and charter situation, the race teams want a new paradigm for the way NASCAR is run. The teams are adamant that they are given a voice when it comes to governance, and they want to create a collaborative environment when it comes to creating new revenue opportunities.

“There’s only a seat if you’re allowed a seat and they’re only going to allow a seat in a few certain situations, but I do think there’s avenues to the drivers being more equitable in the sport in the future,” Hamlin said.

As NASCAR continues to move into legal gambling, the teams don’t want to be cut out of any potential profits. A more recent example is a collaboration announced at the start of the month between NASCAR and Crocs in which five-pack charms are sold separately. But the charms are all licensed specifically for NASCAR — there are no individual team or driver charms, and thus no kickback to the teams.

Polk was adamant that the teams are not asking NASCAR to retroactively compensate for 75 years of how the France family has done business. Instead, Polk said teams are asking “only for incremental revenue.”

“All we’ve asked for is to help make us healthier by giving us a disproportionate share of incremental revenue,” Polk said. “You don’t have to go back into your pockets for what you are used to getting every year. Just the incremental revenue. So yeah, if you’re used to getting $7, we don’t want you to go down to $5. We still want you to maybe get $7.50, but we want a bigger share of this increment to go to us to help us — because we need help.”

The negotiating team said there has been no discussion of creating a breakaway league not sanctioned by NASCAR, and there is no current consideration of staging races at non-NASCAR facilities without NASCAR governance.