In an effort to break the legal logjam that’s threatening their new ballpark, the Oakland A’s are offering to either buy out the city’s half share in the Oakland-Alameda County Coliseum site for $85 million or enter into a long-term lease, sources close to the negotiations say.

The proposed deal also includes a community benefits package and a provision that the team build a new ballpark elsewhere in town, which it’s already planning at the Port of Oakland’s Howard Terminal.

In return, the city must drop the lawsuit it filed to block Alameda County from selling its half share of the site to the A’s.

The site, which includes both the Oakland Coliseum and Arena, is the largest swath of publicly owned land in Oakland and is owned jointly by the city and the county.

Oakland A’s President Dave Kaval proposed the deal to city negotiators at a City Hall meeting Monday afternoon.

The new proposal calls for the city and team to enter into a six-month exclusive negotiating agreement and explore the team’s either buying or leasing the city’s half of the site as part of a larger commercial and residential development.

The project could be done by the A’s alone or in partnership with the city. The team would use the proceeds to build out the Howard Terminal ballpark and associated development.

The new offer also reiterates the team’s willingness to include community benefits such as affordable housing and open space, plus political sweeteners such as labor-friendly contracts, local hiring provisions, apprenticeship programs, and anti-displacement and housing preservation policies.

The A’s have also agreed to pick up the operating costs for the Coliseum and arena, which are estimated to run $15 million to $20 million a year. In return, the team would agree to stay in Oakland and not pursue a possible relocation deal with another city during the six months of negotiations.

If the A’s are unable to deliver on their end of the deal, or unable to come up with a mutually agreed-upon deal for a new ballpark in Oakland — at Howard Terminal or elsewhere — the city would have the right to keep its half of the property and buy back the A’s share if that deal goes through with the county.

But first, the city must drop the lawsuit it filed against the county over the sale of its share in the Coliseum site to the A’s for $85 million and allow the sale to go through. If a deal is not reached on a new ballpark, the city could then buy the A’s half share and wind up with the entire site.

The county wants out of the sports business, and Oakland officials have long wanted the county’s share of the land, but lacked the money to buy it.

Still, some City Council members also feel the A’s went behind their backs by cutting a separate deal with the county. The council asked the city attorney to file the suit to stop the sale and force the county to enter into negotiations to sell the land to the city.

Earlier this month, Alameda County Superior Court Judge Frank Roesch issued a temporary restraining order blocking any immediate sale, but allowed the county to continue negotiations with the A’s. The next hearing on the suit is scheduled for Nov. 14.

The legal block came as a complete surprise to the A’s, who had been in ongoing negotiations with the city over both a waterfront ballpark at Howard Terminal and the Coliseum development deal.

The suit sent the negotiations between the city and the team into a legal tailspin and prompted a pair of private meetings among Major League Baseball Commissioner Robert Manfred, Mayor Libby Schaaf and City Council President Rebecca Kaplan.

Manfred “laid down the law,” according to Councilman Larry Reid, who attended both meetings, telling city officials to make the lawsuit “go away” or risk the team moving elsewhere.

City officials said they would try to resolve the issue by the MLB’s ownership meeting in November.

Last week Schaaf and Kaplan issued a joint statement saying, “We remain committed to working together with the county and the A’s to address the lawsuit and to negotiate a path forward for the Coliseum property that is financially responsible, benefits city residents and is in the public interest.”

Whether the A’s latest offer becomes the “path forward” remains to be seen.

“I’m excited that this framework should help keep the A’s in Oakland and guarantee any future development at the Coliseum site includes affordable housing and critical community benefits for our East Oakland residents,” Schaaf said Tuesday.

Councilman Noel Gallo was encouraged as well

“Absolutely, I think it’s a move in the right direction. It is public land, and we’ll have to sit down and work out all of the details, but I’m a supporter of the A’s staying in Oakland, and that certainly opens the door for us to move,” he said Tuesday.

But Councilman Dan Kalb said he still had concerns.

“If for some reason Howard Terminal doesn’t work out and they do decide to build a ballpark at the Coliseum, then absolutely, positively they should be the master developer and leaseholder, and we work with them to come to an agreement,” Kalb said.

“But if they are not going to build a ballpark there, then why should the A’s get special consideration for the Coliseum site?” he said. “Shouldn’t they just submit proposals like everyone else after seeing what the city wants there?”

Kaplan didn’t respond immediately to requests for comment.

San Francisco Chronicle columnist Phillip Matier appears Sundays and Wednesdays. Matier can be seen on the KGO-TV morning and evening news and can also be heard on KCBS radio Monday through Friday at 7:50 a.m. and 5:50 p.m. Got a tip? Call 415-777-8815, or email pmatier@sfchronicle.com. Twitter: @philmatier