John Lewis' Oxford store has been listed as one of the branches that could close.
The Times published the list, but the company itself has not yet confirmed any locations.
The Times piece says up to 10 of the remaining 18 John Lewis stores which have not yet reopened are at risk.
It comes after new chairman Sharon White told staff in a letter plans to shut several shops, axe one of its two offices in Victoria and cut roles.
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Insiders have been warning recently it was unlikely all 50 John Lewis stores would ever reopen again after lockdown.
John Lewis said: "The reality is that we have too much store space for the way people want to shop now and we have shared this with our partners.
"As difficult as it is, it is highly unlikely we will reopen all ourJohn Lewis stores.
"However no decision has been made and any details would be shared with partners first by the middle of July."
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Sir Philip's Arcadia group also said it was cutting around 500 of its 2,500 head office jobs amid a restructure in the face of the coronavirus crisis.
Luxury department store Harrods is also slashing around 700 posts as the pandemic and lockdown wreaks havoc on Britain's high street.
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