The Oakland A’s have hired the cutting-edge Danish architectural firm, Bjarke Ingels Group (BIG), to lead the design process for a new ballpark and surrounding development.

The firm, which describes its design approach as “pragmatic utopian,” will oversee planning for two possible sites — the waterfront Howard Terminal and the 111-acre Coliseum property in east Oakland.

“We wanted a team that could look at the ballpark with a fresh perspective ... and this is really a game changer,” said A’s President Dave Kaval.

The global architectural firm Gensler, whose projects include the Golden State Warriors’ new Chase Center arena in San Francisco and the just-opened Bank of California soccer stadium in L.A.’s Exposition Park, has also signed on to work on the ballpark design.

For all the excitement over the prospect of glitzy designs, the fate of the A’s new ballpark in Oakland remains far from certain.

Mayor Libby Schaaf raised further questions about how such a deal might be financially structured in a private meeting with Oakland business leaders on Friday. According to sources, Schaaf told the group that the city doesn’t have the money to buy out Alameda County’s half-interest in the Oakland Coliseum site to help smooth the way for a possible A’s development there.

Schaaf told us Tuesday that the picture is actually “a little more complicated.”

“We are fully committed to buying out the county’s share of the Coliseum land, but we will not repeat mistakes of the past by being financially irresponsible when it comes to sports teams,” she said.

It was at Schaaf’s urging, back in May, that the Oakland City Council voted to give the A’s an exclusive nine-month purchase option on the Coliseum site while the team’s management also negotiated with the port about moving to Howard Terminal.

A’s President Kaval, who attended Friday’s meeting at the offices of Oakland developer Michael Ghielmetti, declined to comment on the mayor’s private remarks, saying only that the team stands behind the offer it first made in March to buy out the entire Coliseum site for $137 million.

“We are hoping that offer can be a catalyst to move a privately financed stadium offer forward for the A’s,” Kaval said.

City Hall and other sources tell us the A’s firmly favor building at Howard Terminal, but would still like to win the development rights to the Coliseum property, at the very least to help finance what’s increasingly looking like a very expensive waterfront ballpark.

San Francisco Chronicle columnists Phillip Matier and Andrew Ross appear Sundays, Mondays 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 matierandross@ sfchronicle.com. Twitter: @matierandross