Sheffield was one of eight John Lewis branches the company decided not to reopen post-lockdown last month.
It insists the department store was financially challenged even before coronavirus and bosses are consulting on permanent closure.
Almost 25,000 people have signed a petition to save the shop, formerly Cole Brothers, which was established in 1847.
It employs 299 staff. Further petitions have been launched to save stores that closed this month in Aberdeen, Peterborough, Watford and York, attracting more than 50,000 signatures.
The Sheffield store has been described as the remaining jewel in the crown of a city centre which has suffered challenging times for more than three decades after the opening of the out-of-town Meadowhall Shopping Centre.