Planning permission for the Wentworth Street car park was granted by Ryedale District Council in 2012.
The Fitzwilliam Estate (Malton) won a judicial review against the decision in 2015 which quashed the planning consent.
The council's leader, Linda Cowling, said the authority would now consider what to do with the site.
She said market conditions and changes in the way authorities are funded meant the time was right to drop the scheme.
"Any future plans will be consulted upon, seeking views of our residents and businesses and will include working with other towns and landowners in Ryedale," she added.
The Fitzwilliam Estate had gone to court because it believed its own plans to redevelop the town's former livestock market would have been damaged by the council's proposals.
Mrs Cowling's recommendation to terminate the lease with developer GMI Holbeck Land (Malton) Ltd will be considered by the council on 14 January.
Proposals to build a supermarket on a council-owned car park in Malton, North Yorkshire are being dropped.