Bidders, thought to include McDonald's, KFC and Costa Coffee, are not expected to retain the brand after turnaround firm Rcapital put it up for sale.
Little Chef has gone through a deep overhaul - including a menu revamp by celebrity chef Heston Blumenthal - since it plunged into administration in 2007 and was bought by the London-based private equity group.
But Rcapital said while the chain, famous for its chubby chef logo and "Olympic" breakfasts, has returned to profit, diners have "voted with their feet" and increasingly choose to eat at rival fast food chains.
Rcapital said: "The aim of the sale was to find a buyer that would take the business and the brand on to the next stage. However the market is changing and fast food and coffee houses are growing in popularity. It is not a surprise that the majority of the offers for Little Chef are from companies that may want to rebrand the estate. Rcapital has a deep affection for the Little Chef brand and it is hoped that some Little Chefs will remain on Britain's A roads even if some sites are rebranded."
The Little Chef chain started life as an 11-seat restaurant in Reading, Berkshire, in 1958 and had a string of owners including private equity group Permira. It had 234 outlets with 4,000 staff at the time of its 2007 collapse.
But the chain now has just 1,100 staff at 83 sites from Devon to Scotland, serving about six million customers a year meals including steak and ale pies, fried breakfasts and baked potatoes.
Rcapital added: "Over the last six years, Rcapital has successfully completed an operational turnaround and financial restructuring, which has repositioned the business and brought the group of companies back into profitability. With the turnaround successfully completed it's time to explore the next phase for the food service operator."
Little Chef's turnaround included recruiting Michelin-starred chef Heston Blumenthal to overhaul its menu. The revamp was featured in a Channel 4 documentary, Big Chef takes on Little Chef. It is thought a sale will not be complete until the end of the summer. Rcapital has appointed KPMG to sell it.