His private equity firm Hamilton Bradshaw is carrying out due diligence checks on the group, according to the Daily Telegraph. Little Chef was put up for sale by owner Rcapital in April.
It was reported last month that bidders including McDonald's, KFC and Costa Coffee were considering making an offer, but ditch the brand, which would see its Fat Charlie mascot disappearing from the roadside after 55 years.
Sources close to Mr Caan told the Telegraph that he was interested in saving the brand and expanding it in the UK, possibly securing many of its 1,100 jobs. The newspaper also reported that it could result in the franchise being expanded to the Middle East.
It is understood the expansion in the UK would include mobile sites on A-roads as well as fixed restaurants.
But it is believed Mr Caan does not want to buy all the Little Chef outlets and is prepared to work with another bidder. He is said to be eyeing an offer in the range of between £10 million and £15 million. However, sources close to the sale process said potential offers had already been received in excess of £20 million for the whole business.
Famous for its large "Olympic" breakfasts, Little Chef had 234 outlets with 4,000 staff at the time of its 2007 collapse. But the chain now has just 83 sites from Devon to Scotland, serving about six million customers a year meals including steak and ale pies, fried breakfasts and baked potatoes.
Mr Caan, the Government's new social mobility tsar, was plunged into controversy this week after an interview in which he argued parents should not give their children a helping hand in finding jobs - only for it to emerge that he had employed his two daughters.
Hamilton Bradshaw was not immediately available for comment and Rcapital declined to comment.