The owner of Yo! Sushi is battling rival private equity firms to acquire Byron, the upmarket burger chain, for £100m.
Quilvest, which acquired the sushi chain in 2008, and Searchlight Capital Partners are understood to be among the private equity houses through to the second round of bids for Byron.
Byron is owned by Gondola Holdings, which has teamed up with DC Advisory for the sale. The burger company nearly doubled pre-tax profits to £2.2m, on sales of £28.6m, over the year to July 2012 and is forecast to post underlying profits of more than £10m this financial year.
Gondola, which is controlled by the private-equity firm Cinven, also owns the Pizza Express, Zizzi and Ask chains.
Tom Byng founded Byron in 2007 after four years in the US during which he ate "enough hamburgers to sink the Titanic".
All parties declined to comment.