Alameda County supervisors, hoping to keep the A’s in Oakland, agreed Tuesday to negotiate the sale of their share of the Coliseum complex to the city of Oakland.

Supervisors said they were encouraged by the A’s expression of interest two weeks ago in buying the Coliseum site to build a stadium and develop the area around the existing stadium and Oracle Arena.

A’s President Dave Kaval sent Oakland Mayor Libby Schaaf and the City Council and the Alameda County Board of Supervisors a letter March 25 weekend with an offer to pay off the nearly $137 million in debt owed by the city and county on the Coliseum in exchange for full control of the site.

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Schaaf quickly expressed support for the idea, though she didn’t agree to the terms of the A’s offer. East Bay officials have rallied behind the idea, which could keep the A’s in Oakland, despite the Laney College faculty’s rejection of the team’s proposal to build a stadium next to their campus.

The Coliseum is owned and managed jointly by the city and county, and the board believes having a single owner would make it easier to negotiate a sale, said supervisors Scott Haggerty and Nate Miley in a statement.

Because the city controls land use at the site, the supervisors said, it makes sense for Oakland to become the sole owner and bargain with the A’s for the property, the supervisors said.

Oakland and Alameda County have owned the Coliseum complex, including the stadium, arena and sprawling parking lots, for more than 50 years. They’ve been home to the A’s, Oakland Raiders and Golden State Warriors, whose success prompted officials to name the complex the “Home of Champions.”

In addition to keeping the A’s in Oakland, the supervisors hope the sale of the Coliseum will spur development of the area, which sits aside Interstate 880 and a short walk from BART and the Capitol Corridor rail line.

“Negotiating the sale of the county’s share will enhance the city’s abilities to pursue its vision for substantial new development at the Coliseum site,” the statement said.

Michael Cabanatuan is a San Francisco Chronicle staff writer. Email: mcabanatuan@sfchronicle.com Twitter: @ctuan