The former Yorkshire Bank building at the top of Fargate has been empty since October last year.
The bank rented the basement, ground and first floors and has hired a commercial agent to find a new tenant.
Gary Crompton, director at Baker Proudlove, said he was in ’serious’ discussions with two national restaurant companies over the space.
But even if a deal were struck, a new venue would not open this year, he added.
Virgin Money, the new name for Yorkshire Bank after a merger last year, continues to pay rent to building owner Fargate Properties. The lease runs until 2035.
The upper two floors are marketed by Lambert Smith Hampton.
EMPTY SHOPS ON FARGATE
About a quarter of the 40 shops on Fargate are empty.
But there are signs of regeneration, including the former Next which is undergoing a £1.5m refurbishment.
In June, the owner revealed two national restaurant companies had shown an interest - raising the prospect of a bidding war.
The unit, at the corner of Norfolk Row, has been empty for more than a year after Next moved to The Moor.
The entire street is set for a revamp after the city council won £16m from the Future High Streets Fund.
Earlier this week, The Star revealed restaurant chain German Donor Kebab is set to open in Telegraph House on nearby High Street.
Yorkshire Bank staff moved into the Virgin Money premises opposite following the merger last year.