The tug-of-war between the city of Oakland and Alameda County over the county’s proposed $85 million sale of its half share in the Coliseum complex to the A’s appears headed to a legal showdown.

The city, which also owns 50% of the site, says it should get first dibs on buying the county’s share of the 155-acre site. The county has responded by basically telling the city to put up an offer or shut up.

At issue is a deal being negotiated whereby the county would sell the A’s its half interest property, including the Oakland Coliseum and Oracle Arena. The A’s would then build a business park and housing development, with the profits to be used for the team’s privately financed waterfront ballpark at the Port of Oakland’s Howard Terminal.

Oakland, however, is saying not so fast.

In a letter delivered to county officials Monday, Oakland City Council President Rebecca Kaplan and Vice Mayor Larry Reid noted that the deal between the county and the baseball club lacked any provision for building a ballpark for community benefit to be included in the sale.

The letter ends with the request for the county to “clarify” whether it planned to go forward with the A’s sale, so that the city could “determine effective next steps.”

The city’s letter made no mention of what the “next steps” might be, but a separate Aug. 31 email to Oakland City Attorney Barbara Parker said the letter is for “the purpose of potential litigation.”

Some City Council members have said privately that they feel the A’s request to — in effect — control both the Coliseum and Howard Terminal sites is too sweet of a deal for the team.

Some council members, including Reid, want the team to stay at the Coliseum site.

“I’ve always let it be known that I preferred the A’s to build at the Coliseum,” said Reid, whose district includes the site.

“This is about money,” Alameda County Supervisor Scott Haggerty said. “The city wants more community benefits from sale, and this is a way to get us to the table and negotiate.”

The county has long wanted to get out of the sports business, so when the A’s made an offer this year to buy out its share of the site, supervisors jumped at the prospect of a sale.

But, as the negotiations with the A’s are not exclusive, the city could still make an offer.

Whatever the case, within 24 hours, Alameda County Board of Supervisors President Richard Valle responded the to the city’s letter with his own, detailing 33 meetings and pieces of correspondence with Oakland politicians and city staff since 2015 regarding the city buying out the county.

Most recently, Valle said, the county presented a term sheet for a possible sale to city staff on Feb. 25; it has yet to get a response.

One big issue: money. Oakland doesn’t have $85 million to spare.

“But if we were given the same time frame as the A’s to pay it, which I understand is something like 10 years, we could work something out,” Reid said.

San Francisco Chronicle columnist Phillip Matier appears Sundays and Wednesdays. Matier can be seen on the KPIX-TV morning and evening news. He 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