The first two proposals in Chambers Street may be open within two years.
Others could follow at locations including George Street and the Grassmarket.
Edinburgh City Centre Management Company (ECCMC) chief executive Gordon Reid said: "We are still at the feasibility stage and have not yet carried out a detailed site investigation at Chambers Street, but it is fair to say that it is the favoured location for the pilot project." Applications could be lodged early next year, he added.
The proposal to introduce low-impact, computer-controlled car parks is contained in the Edinburgh city centre action plan, which aims to improve access to the capital. Each location would hold around 100 vehicles, lowered into bays and retrieved automatically after motorists pay at a computer panel.
The ECCMC is working with Trevipark Ltd, the company behind similar schemes in Rome, Turin and Milan.