Last spring, a deal fell apart because of financing issues.
London's Gatwick Airport just went through the process but it was sold at a significantly lower price than expected. With that in mind, the mayor says he's willing to wait until the economy stabilizes.
"Cities have done this all over the world. This is a very progressive legislation. You have to understand that. It's very progressive," said Daley.
Midway employs 190 people who are paid by the city.
If the mayor does try once again to privatize the airport, aldermen are expected to study the lease very carefully considering the negative fallout from the parking meter lease deal.