There has been plenty of interest from prospective tenants looking to move into a former coffee shop.
Costa Coffee relocated from its former premises in London Street to a biggerstore at the bottom of the road opposite Jarrolds in the autumn.
Chartered surveyors Roche has confirmed the former Costa site - which is located next to Greggs - is currently under offer.
Roche partner Adrian Fennell would not disclose who has enquired into moving into the building.
Mr Fennell would also not reveal an anticipated timescale for when the site will be occupied again.
He said: "There have been many enquiries. It's under offer but I am not going to say anymore than that.
"Hopefully the outcome will be a positive one for the owner."
The Costa branding has been removed from the former shop at 48 London Street where there is a small amount of graffiti in the doorway.
Costa now has a presence in the large corner plot which used to be home to Jack Wills.
The national chain has been busy since opening despite competition from other big brands such as Caffè Nero and Pret A Manger nearby.
Professor Josh Bamfield, director of the Centre for Retail Research in Norwich, said there has been a "rapid expansion" of high street coffee over the last 20 years.
Experts in his industry questioned whether 2010 could be when coffee culture had reached its peak - but the demand has shown no signs of slowing down since.
Prof Bamfield said: "There has been an inestimable demand for coffee but they nonetheless seem to be pretty successful.
"I do not see any reason why Norwich can't cope with even more coffee shops.
"You see a lot of people sat inside drinking coffee but the amount of people carrying takeaway cups also goes to show just how obsessed people are."
He believes national chains are a success in city centres because tourists "like the familiarity" of the menu and interior.
But he also highlighted the popularity of independent shops in the market and Norwich Lanes.
A Costa spokeswoman said: "Since the opening, which saw all team members transferred over to our new store, we have been busy serving customers."
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