Hoping to rustle up much-needed cash, the New York City Housing Authority unveiled a plan Monday to lease millions of square feet of its property to private developers for mixed-use construction of housing and retail space. The plan to turn what are now parking spots, walkways and parks into at least 1,000 units of affordable housing, along with market-rate housing and commercial and retail development would not displace any public housing residents, nor result in the demolition of any Housing Authority buildings, Chairman John Rhea said at a breakfast forum Monday hosted by the Association for a Better New York. Some of the revenue generated from the development is expected to be reinvested locally at the sites where the construction is taking place. No sites have been selected, but multiple locations will be available to developers. Mr. Rhea said that Manhattan would be the most likely place to start. He predicted that money could start flowing into the Housing Authority by the end of 2013.