With a year left on American Airlines’ original sponsorship deal for the Miami Heat’s arena on Biscayne Bay, Miami-Dade on Tuesday decided to take over talks for the next naming-rights agreement for the county-owned building.

The Heat privately opposed the move, which is allowed under the team’s 2014 updated lease for the county arena. The existing arena deal costs Miami-Dade about $5.5 million in annual subsidies, and the county receives almost no revenue from the $2 million that American pays the Heat each year to be the public building’s title sponsor under a naming-rights deal first struck in the 1990s.

County consultants expect the sponsorship to at least triple in value once the American deal expires at the end of 2019. Miami-Dade is exercising its option to end the Heat’s current exclusive negotiations with the airline in favor of a broader search for sponsors.

“We think it’s a very good opportunity for us to make a lot more money than we make now,” said Mayor Carlos Gimenez, who negotiated the 2014 extension of the Heat’s original county deal from the 1990s to build the waterfront arena. “I’ve already fielded some calls. There’s a lot of interest in naming the arena.”

American has already reached out to the Gimenez administration about remaining as the arena’s sponsor. The Texas-based airline began negotiations with the Heat earlier this year to extend its current naming-rights agreement, said Ed Marquez, the county’s chief financial officer.

In a statement released after the County Commission vote approving the change, American said: “We support the resolution approved by the Miami-Dade County Commission. … With that said, we are also hopeful that we can retain the naming rights to the arena.”

The Heat issued a terse statement that said in part: “Several weeks ago, the County administration called to inform [the Heat organization] of its intent to recommend that the Commission exercise its option to sell the naming rights. … In deference and good faith to the County’s efforts to sell the naming rights, we will not have any further public comment on this matter.”

By taking over the sponsorship talks, the county will end American’s current negotiations with the Heat and start fresh with a consulting firm that will earn a 5 percent commission on whatever deal is secured for the government-owned building. Miami-Dade had until the end of 2018 to exercise its option, or let the Heat negotiate the arena’s next naming-rights deal under more favorable terms for the county.

The consultant, Cleveland’s Superlative Group, describes the current American deal as a bargain, particularly given the Miami arena’s standing in the market.

While built in the late 1990s on a largely desolate stretch of Miami’s downtown waterfront, the arena now faces luxury high-rises and sits next to new county-funded museums. The departure of LeBron James in 2014 ended the arena’s white-hot era, but Pollstar still ranks the “AA Arena” as the highest-grossing entertainment venue in Florida, and one of the Top 10 nationwide, according to a county memo.

American pays $6 million a year to sponsor its other NBA stadium, where the Dallas Mavericks play. In Oakland, JP Morgan’s 2018 sponsorship deal for the new home of the Golden State Warriors (and Stephen Curry) costs $15 million a year, according to a county memo.

Superlative Group’s Myles Gallagher said a new sponsorship deal in Miami should bring at least $6 million a year. “Six million is very conservative,” he said. “We’re not discussing what we would put it to market at, because we don’t want that to become public record.”

By exercising its naming-rights option, Miami-Dade must pay the Heat an additional $2 million a year starting in 2020 to make up for the money the team currently receives from American Airlines. That payment from Miami-Dade to the Heat will be due even if the county doesn’t line up another brand willing to pay to put its name on the arena. Anything over $2 million, the county gets to keep. The Superlative commission is paid on the county’s portion of the naming revenue for the 19,600-seat arena.

Miami-Dade’s original 1997 deal with the Heat allowed the team to sell the naming rights for the county building. The revenue from American offset what was supposed to be an $8.5 million yearly subsidy by the county to the team.

Instead, the payment from county hotel taxes amounted to roughly $6.5 million. It remains at that level today, except that under the revised 2014 terms, the team now makes a $1 million donation to the county parks department each year.

Granting the county the option to sell the arena’s naming rights was a concession by the Heat during the 2014 talks, which extended the original 1997 subsidy deal five years into 2035. For those additional five years, Miami-Dade’s Heat subsidy will increase from the existing $6.5 million to $8.5 million.

Under the 2014 deal, the Heat must provide certain benefits to the arena’s sponsor and cooperate with the county on a deal, including painting the name of the brand on the basketball court. But the decision on the arena sponsor will ultimately be up to the 13-member County Commission.

That sets up the possibility of a competing cruise ship company bidding to put its name on an arena that’s home to a basketball team owned by Carnival Chairman Micky Arison — or Carnival could bid on the deal.

Jose Galan, the county real estate manager who oversees the arena, cited “cruise lines, car-rental agencies” as examples of the kind of major companies that might be interested in naming rights.

Heat representatives did not speak at Tuesday’s commission meeting and were not available for comment Tuesday afternoon. An American representative also was not available for an interview.

Behind the scenes, the Heat lobbied the county to let the team continue its talks with American and then simply share a portion of the naming proceeds over $2 million with Miami-Dade. That’s allowed under the 2014 agreement, too, but the Gimenez administration argued it would cost the county millions to share the proceeds with the Heat.

“They’re completely against what we did,” Commissioner Audrey Edmonson, whose district includes the arena, said of the Heat’s front office. “I don’t blame them. I would want the naming rights as well. But since it’s a county building and county land, I think it’s time the county start thinking about itself.”