It would be a “shame” if developer Larry Silverstein couldn’t build one of his proposed World Trade Center office towers, but the city is unlikely to step in with subsidies, Mayor Bloomberg said yesterday.

“We’re not in the business of supporting commercial real estate,” the mayor said in response to reports that Silverstein still has not identified the tenants he needs to pre-lease 10 of the 80 stories proposed for 3 World Trade Center. Without those tenants, the building may wind up with just seven floors.

“We . . . remain fully optimistic that we will sign a lease in time to complete the tower as scheduled in 2015,” Silverstein said.