Morrisons had agreed to rent the 73,000 sq ft store but the site developer said its lawyers were now attempting to "terminate the agreement".
Augur Buchler Partners (ABP) Ltd said it had received notice from Morrisons on 16 December and the matter was "being dealt with by our lawyers".
Morrisons has so far declined to comment on their plans for the site.
On Tuesday, the supermarket giant said its chief executive was to leave after five years in charge, and it would be closing 10 loss-making stores during 2015.
Cheltenham Borough Council, which sold the land to ABP in 2011, had wanted to develop the car park since 2008 with previous ideas including a new library, flats, homes and retail space.
But the plans were put on hold due to the recession.
Councillor Andrew McKinlay, cabinet member responsible for built environment, said the latest setback was "certainly disappointing news".
He added: "It's important to say at this stage we're not going to do anything too quickly because, until the dust settles and we know exactly what the situation is, I think it would be unwise.
"Clearly, we need to get the Morrisons legal situation resolved before we can move forward on any other potential plans."
The construction of the £60m redevelopment was originally expected to be completed in late 2015.
The council's pay-and-display car park was shut last year and work has already begun to dig up the ground.
A major project to redevelop a Cheltenham town centre car park into a new supermarket has been suspended.