The producers of the television spy series Burn Notice are optimistic the show will get picked up for a seventh season.

They are less confident they will continue shooting in Miami.

It’s not that Burn Notice wants to leave. The producers have asked for a year-long extension on their lease at the city-owned Coconut Grove Convention Center. They have filmed on the site since 2006.

But Miami Commission Vice Chairman Marc Sarnoff is holding firm on his promise to demolish the convention center and turn the grounds into a waterfront park. At least two other commissioners seem supportive of Sarnoff’s initiative.

Sarnoff, who has been an advocate of the film industry locally, hopes Burn Notice will consider shooting elsewhere in Miami.

Studio executives, however, say that’s unlikely.

“If we don’t have the Coconut Grove Expo Center, we will not be filming Burn Notice in the city of Miami,” said Bob Lemchen, the head of production for Fox Television Studios. “It’s just not an option for us.”

Burn Notice, which airs on the USA network, centers on former spy Michael Westen, who is stuck in his hometown of Miami after the CIA scrubs his identity and freezes his assets. Westen and his posse traipse around South Florida trying to figure out who burned him. Along the way, they use their spy savvy to help South Floridians who run afoul of mob bosses and other shadowy figures.

The home base for production is the old Coconut Grove Convention Center. The show pays the city $240,000 in annual rent on a lease that expires in October.

If Burn Notice is picked up for an additional year, Lemchen says the show would be willing to pay a larger rent to stay in the convention center. Lemchen pointed out that the show is built around filming in Coconut Grove, and that scenes often feature local attractions, landmarks and restaurants.

“The show brings Miami alive as a character,” said Eduardo M. Freyre, a Coconut Grove actor who has worked as a Burn Notice extra.

Sarnoff doesn’t deny the value of having a television show filmed in his commission district. But he says the residents of Coconut Grove have made it clear at public hearings that they want a park.

What’s more, he says, the city has stashed away $1.8 million in Burn Notice rent payments and grant dollars.

“This is the front door to Miami. Right now, you are looking at burned-out cars, concrete and trailers,” Sarnoff said.

Other commissioners have suggested Burn Notice move to another Miami film-production studio. Commissioner Michelle Spence-Jones, for one, wants production to move to a facility in the Wynwood neighborhood.

“I definitely think it would help revitalize the area,” she said.

But Burn Notice producer Terry Miller said the facilities in Wynwood are “too raw” and would require costly improvements to the roof, air conditioning and electrical systems.

Miller said he has scouted out other Miami facilities, and none are suitable for Burn Notice. Even with the right location, Lemchen said, it would cost at least $1 million to move to another studio.

“We will continue looking at Miami,” Lemchen said. “But we’ve had more success looking at Broward, and other states remain a possibility.”