Part of the discussions could center on the ownership of the stadium, which sits on county land but currently belongs to the Dolphins. A possible deal, for example, could involve giving ownership of the facility to the county, with Miami-Dade providing an operating subsidy to the team. A similar arrangement exists between the county-owned AmericanAirlines Arena and the Miami Heat.

Commissioners enumerated several wish-list items Wednesday, including guaranteed local hiring and a commitment to holding future, potential Super Bowl events — and the Dolphins’ training camp — in Miami-Dade, not Broward, if Broward does not fork over any money toward the deal.

Foreseeing the renovation push this year, the Dolphins and team owner Stephen Ross, through third-party political committees, contributed heavily last year to the reelection campaigns of Gimenez and four incumbent commissioners. Gimenez also attended a Dolphins game last year as a guest of the team.

Longtime lobbyist Brian May, a one-time aide to former Miami-Dade Mayor Alex Penelas who has led the County Hall advocacy effort for the Dolphins and raised money for Gimenez’s campaign, said all the ties to the incumbent mayor are not surprising.

“There are a lot of people who worked on the mayor’s campaign because he was going to be the winner, frankly,” a wry May said. “Funny how that works.”

Among the other familiar political faces involved: longtime Dolphins lobbyist Ron Book; attorney H.T. Smith, who is advising the team on strategy; and Penelas.

Penelas, another strategy advisor, appeared on a Spanish-language radio station earlier this week praising the team’s proposal — but did not disclose his advisory role. In an e-mail, Penelas declined to comment about his relationship with the Dolphins, citing his contract as a commentator for the Spanish-language Univisión network.

“We have assembled a diverse and experienced team with strong local knowledge to help advise us on this complex issue,’’ Dolphins spokesman Ric Katz said in a statement. “We believe this is enabling us to reach and engage all segments of the Miami-Dade community.”

The Dolphins have also garnered the support of other influential County Hall figures: Rodney Barreto, May’s lobbying partner and chairman of the Super Bowl organizing committee, and Ralph Garcia-Toledo, head of the exploratory committee to bring the Pan-American Games to Miami. Garcia-Toledo, an early Gimenez supporter, frequently drove the mayor to campaign events during Gimenez’s successful 2011 and 2012 races.