Will Southdale become a place to shop, sweat — and swim?

Life Time is considering adding a fitness center in the space currently occupied by J.C. Penney.

The proposed fitness center would be 120,000 square feet and have a pool on the roof, according to plans submitted to the city of Edina.

Jason Thunstrom, Life Time spokesman, said that the Chanhassen-based fitness company is beginning to consider nontraditional models for new locations. “With the wave of anchor-store closings, we’re working with a number of property management groups,” he said.

The plan is still short of a number of approvals needed. “It’s too early to say if it will be J.C. Penney definitely. It’s very preliminary,” he said.

Representatives from Simon Property Group, the owner of Southdale Center, said there is a pending deal, but the full picture won’t be known for a couple of weeks. Penney’s is still operating in Southdale, and the location wasn’t listed among nearly 140 stores the Dallas-based retailer is closing in the next several months.

Life Time has recently considered nontraditional locations in other markets. In Oklahoma City, Okla., it took over a former Macy’s in Quail Springs Mall. It has a two-level facility under the main floor of Target Center in downtown Minneapolis.