Wheeler's comprises six outlets in London and one in Brighton. Others up for sale are two Eatons Wine Bars, the Dickens Inn at St Katharine's Dock and the Issimo restaurant in Lime Street, all in London, and the Kings Head in Ivinghoe, Buckinghamshire.
Offers are invited by April 12 through Christie & Co.
The outlets are part of Compass's Select Service Partner (SSP) division.
It will re-invest the proceeds in developing new sites for SSP.