The site opened with 190-covers in 2016 and offered "British tapas" plates, an a la carte and seven-course tasting menu.
But owner Paul Roden told the Manchester Evening News he and his wife Kathryn were selling the site to another operator, who plans to reopen it as a "high-end gastropub-style" concept.
He said that though the Grafene could serve "over 100 covers on a good night" it had struggled in a "difficult market".
The restaurant shut its doors last weekend, but will reopen at the Roden’s Losehill House Hotel & Spa in the Peak District where it will replace the existing dining offer.
Grafene’s closure follows the demise of two high-profile Manchester fine dining restaurants last year.
GG Hospitality closed The Rabbit, formerly Michael O’Hare’s The Rabbit in the Moon, in November after the company said trading figures “[did] not justify keeping the operation open”.
Living Ventures also shut Manchester House following “difficult trading”, but the restaurant was bought out of administration and relaunched by Aiden Byrne and a group of investors in December.