According to The Telegraph, the Brewer Street site could be taken on by contemporary Mexican chain Tortilla Republic, which states on its website that a London location is coming soon.
The closure would mark the cessation of Hix’s presence in the West End of London.
Last year the chef restaurateur told BigHospitality’s sister site FoodSpark that he had ruled out opening any further restaurants in the capital, citing excessively high rents.
He said: “Soho landlords have almost doubled our rent and business rates.
“It’s becoming more and more difficult to operate and turn a profit.”
The Telegraph reports that Hix plans to turn his attention to Dorset, where he grew up.
His Oyster & Fish House in Lyme Regis is believed to be doing well, and he is understood to be considering a venture in Weymouth, where he supports training courses for young chefs.
Hix opened his first solo site, Hix Oyster & Chop House, in Farringdon in 2008, which he continues to operate alongside chicken and steak restaurants Tramshed and Hixter Bankside in the capital.
He also has two Mark’s Bars in London beneath his HIX Soho and Hixter restaurants respectively, and owns a subterranean art space below Tramshed.