OAKLAND — The Oakland A’s have offered to buy Oakland’s ownership share of the Coliseum complex for $85 million — a gesture that could thaw a frosty relationship and ultimately result in the team redeveloping the site.

The baseball team wants to convert the complex, jointly owned by Oakland and Alameda County, to a mixed-use development to help it finance construction of a 35,000-seat ballpark along the estuary near Jack London Square.

Alameda County earlier this year agreed to sell its half of the site to the A’s — also for $85 million — but the city blocked that maneuver by suing the county. As part of its offer, the A’s want the city to drop that lawsuit.

In its offer to the city, the A’s also agreed to build affordable housing at the Coliseum property, use local labor and provide other yet-to-be-determined community benefits.

A’s president Dave Kaval said in an interview Wednesday the A’s also offered Oakland the option to lease the land to the team as a “joint venture” rather than selling it.

“We want to show flexibility, so that the city understands that we want to work towards an amicable partnership and not deal with this in a courtroom,” Kaval said.

Kaval said he hopes the city will agree to enter into an exclusive negotiating agreement with the A’s for its share of the Coliseum complex. During that period, the two sides can work out details, such as how much affordable housing to build, he said.

He said he also hopes the city will drop its lawsuit against the county before Nov. 17 — the date of the Major League Baseball owners’ meeting. League commissioner Rob Manfred had asked Kaval to provide an update on the lawsuit’s status at that meeting, Kaval said.

The lawsuit, filed last month, seeks to block the county from selling its half-ownership share of the Coliseum site to the Oakland A’s, which could complicate the city’s efforts to one day redevelop the site. The lawsuit alleges the sale would be illegal.

Councilman Larry Reid said he also hopes the city will drop the lawsuit. The next court hearing on the suit is scheduled for Nov. 14. Reid said he’s glad the A’s made an official offer but hasn’t yet decided whether he will vote to take it.

“It’s a step in the right direction,” Reid said in an interview Wednesday. “Hopefully there’s some consensus amongst us (council members) based on the offer.”

Before the lawsuit was filed, Reid and City Council President Rebecca Kaplan had written a letter urging the Board of Supervisors to negotiate selling the county’s share of the Coliseum to the city instead of the team. They wanted the city to have greater say in the future of the site and noted it would make more sense for the city to be the sole negotiator with the A’s since the Coliseum is in Oakland.

The offer doesn’t come as a surprise to at least some city officials: Kaplan has said she suggested to both Manfred and the A’s that the team should present an official proposal to the city so all parties could potentially work out a deal.

Kaplan, in an interview Wednesday, called the A’s new offer “positive progress.”

“Some had worried that we would have to choose between either working with the A’s or having a project with affordable housing and other community benefits,” Kaplan said. “It has been my hope that we could have an option that would allow for both things to happen — and that is looking like a good possibility.”

The city’s negotiating team will present the A’s offer to the council during a closed session Tuesday, Reid said, though it’s unlikely there’ll be a vote that day.

This story is developing. Check back for more information.