Councilwoman Angela Hunt said the city may have overlooked possible uses for the site. The Parks Department has a shortage of indoor soccer space and is seeking to build more facilities, Hunt said. But the department has not been approached about the possibility of reusing Reunion Arena.
"I think we should explore every avenue of reusing it and think about it before we destroy it," she said.
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The demise of the 28-year-old arena was sealed in 2001 when the Dallas Mavericks and the Dallas Stars moved their games to the new American Airlines Center.
Dallas officials said the city has lost millions of dollars trying to keep Reunion Arena open with the sharp decline in events.
City Council members voted last June to permanently close the building and seek bids for demolition. The low bid is just over $2 million.
"It's with mixed feelings, but sometimes you have to cut your losses," said Councilman Pauline Medrano, whose district includes the Reunion Arena site.
The city plans to keep the land in hopes of future development there.
"I'm looking forward to seeing ideas that will bring people to downtown," Medrano said.