According to an email seen by the BBC, the owner of dining chain The Restaurant Group (TRG) is set to tell staff on Wednesday that many sites are "no longer viable to trade and will remain closed permanently".
The email adds: "The Covid-19 crisis has significantly impacted our ability to trade profitably, so we've taken the tough decision to close these restaurants now."
Although it is not clear how many sites will be affected, the BBC says the message was sent to managers in the group's Leisure Division, which consists of more than 200 Frankie & Benny's restaurants.
There are three Frankie & Benny's restaurants in Leeds at Cardigan Fields, The Light and White Rose Shopping Centre and one in Birstall,
The BBC says TRG declined to comment on the report.
In March, TRG was forced to shut a majority of its Chiquito Mexican-style outlets as well as its Food & Fuel chain of pubs in London after falling into administration.
The company, which also owns Wagamama and Garfunkel's, is one of the largest restaurant operators in Britain.
It currently has around 22,000 staff on furlough.
Imminent Frankie & Benny's closures were already announced by TRG in February, with the company saying it planned to shut up to 90 restaurant sites by the end of next year.
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