Mr Frost, 54, who has twice sold filling station chains to the majors, said he has invited his rivals to "come talk to me and we'll see if we can do a deal".
Selling could make a tidy profit for Mr Frost, who owns about 4.5 per cent of Save - 650,000 shares and options to take 4 million more. In 1980 he sold 50 stations for pounds 50m to Elf Aquitane. In 1990, Norfolk House Group paid him pounds 60m.
"We've talked to a number of people who have approached us," he said. "I can't say if any of those discussions are live."
Save Group, which last week changed its name from Frost Group Plc, has a market capitalisation of pounds 91m and made pretax profit of pounds 10.4m last year.