More than a dozen firms are bidding to build the subterranean facilities in front of the Royal Museum which would see vehicles lowered underground and parked automatically.
However, officials have stopped work on assessing the bids after lawyers were called in to check who owns the land on Chambers Street.
Sources close to the project claim the land ownership issues – as well as concerns about the impact it would have on a multi-million-pound revamp of the Royal Museum – have put the scheme in the balance.
If Chambers Street proves to be too difficult then it is thought the focus will switch to building one of the car parks under George Street.
Council chiefs today insisted they were still committed to the scheme but had suspended the tendering process while legal issues are ironed out.
They have drafted in lawyers to check land ownership issues after concerns the street could be "common good" land and the council may face a legal challenge if it tries to use it for what would be a commercial development.
Councillor Phil Wheeler, the city's transport Convener, said: "Plans for an underground car park in Chambers Street remain very much alive, and we are looking forward to resolving the outstanding legal issues."
Community and motoring groups today urged city leaders to abandon it altogether.
Bruce Young, the Lothian and Borders co-ordinator of the Association of British Drivers, said: "
The Southside is short of suitable parking but something like this, which will undoubtedly be more expensive, is more suited to somewhere more central. I would have thought George Street would be more appropriate.
"Better still, the council should look at the various parks and gardens across the city.
"There would be far less on-street disruption, and it would be possible to put the parks back to their old condition afterwards."
The car parks were first suggested in 2005 by the Edinburgh City Centre Management Company, but the project has now been taken over by the city council.
The existing 89 parking bays would be replaced by 100 underground spaces built on either side of the William Chambers statue.
Motorists using the facility would pay on arrival and get out of their vehicle. A computer-controlled lift would then automatically take the car underground, and put it in a parking bay. When the owner returned, the car would be automatically brought back up for them.
It is thought construction of the car park would take around 18 months and involve severe disruption to Chambers Street.
Bill Cowan, of the Grassmarket Traders' Association, said: "We will be glad to see the back of this underground car park idea.
"They want to create all this disruption in the historic heart of the city for the sake of gaining something like ten parking spaces."