Councillor Patrick Harley, leader of Dudley Council, said interest had been expressed in turning the former Dudley Museum and Art Gallery into an entertainment venue.
The imposing red-brick building on the corner of St James's Road and Priory Street has been lying empty for more than four years since the museum closed.
Councillor Harley said such a development would be a welcome boost to the area, and would represent an opportunity to boost the Stone Square area of town.
"We have had interest in turning the museum into a wine bar and upmarket cocktail bar, and when you look at how popular that sort of place is at the moment, you could see it bringing a lot of people in," said Councillor Harley, who himself works in the licensed trade.
"Just across the road you have got The Old Glasshouse, which is a nice restaurant, and you have got the Saracen's Head on the opposite side of the square.
"If we could then utilise some of the other buildings around the square, you then have the start of a lively little leisure quarter, with a good night-time economy.
"That then spreads out to some of the other businesses around the town," he added.
The gallery building, well known for its meteorological instruments outside, was opened in 1883 by Earl Beauchamp, the Lord Lieutenant of Worcestershire as an art school and library.
The art gallery itself opened five years later, and a geological museum was added in 1912.
The Brooke Robinson Museum, which had previously been located next to the town hall, was moved into the building in 1981, and a collection of memorabilia relating to Dudley-born football legend Duncan Edwards was also added.
It once displayed works by impressionist J MW Turner, as well as renowned Black Country artist Percy Shakespeare.
But the venue closed in December 2016 as part of a plan to save £150,000 a year.
Some of the exhibits were moved to the new Dudley Archives Centre in Tipton Road, and others were put on display at Himley Hall.