Dino Ferrari, known as Dino's, in Sauchiehall Street will shut its doors on Sunday, March 16, the Evening Times understands.
The Italian restaurant has been a favourite of city centre diners for more than 50 years.
A Halifax spokeswoman said: "Following the successful opening of our Aberdeen branch in December 2013, this year we will also be opening Halifax branches in Glasgow and Edinburgh.
"These branches will be in central locations within the city centres and we look forward to providing further details as soon as we are in a position to do so."
The opening of the new Halifax is not expected to affect the Bank of Scotland branch at 63 Sauchiehall Street, directly across the road from Dino's.
Nobody from Dino's was available to comment officially, but a member of staff confirmed that the expected closing date for the restaurant would be March 16.
Dino's in its original form was opened by Swiss-Italian Francis Ferrari at 10 Sauchiehall Street in the 1960s, before Dino Baldi opened his restaurant in Buchanan Street in 1966.
Soon after, Mr Baldi also acquired Ferrari's restaurant and Dino Ferrari was born, with the business eventually moving to 35-41 Sauchiehall Street where it has been based for more than 30 years.