The Little Chef chain of restaurants is to be broken up, and the brand name so familiar to British motorway users could disappear, said the Sunday Times.
Last year Little Chef considered slimming its chef logo down
Its owner, private-equity firm Permira, plans to sell 120 of the 235 restaurants.
British motorists tend to associate the roadside cafes with fried food. Permira - which bought the chain in 2003 - has found it hard to turn round.
But Permira said on Sunday there was still value in the Little Chef name.
"Little Chef is a strong brand name in the restaurant sector with a loyal customer base and an unparalleled network of UK roadside restaurants," its Little Chef board said in a statement. It added that it was seeking to sell off 120 Little Chef sites "as a going concern".
We are "seeking to identify a buyer that is better placed to maximise its growth potential in the longer term," it said.
The company added that there had been "substantial interest in Little Chef from a variety of UK and international companies."
It said it would continue to run its remaining restaurants under their existing brand name.
"It is our intention to agree with the new owner that we continue to operate the Little Chef brand," said the company.
In August last year, the company tried to slim down the Little Chef used in its logo but was forced to do a U-turn when customers complained.
Little Chef began life in Reading, Berkshire, in 1958 and expanded along with Britain's trunk road network.
The chain is thought to be suffering from competition from roadside fast food outlets like McDonald's which serve customers more quickly.
It is possible that its rivals may be interested in acquiring some of Little Chef's sites.
So there could be fewer plump Little Chefs decorating our roadsides in future.