The source added that a second round of bids for the Areas catering business was also underway.
A separate source had earlier told Reuters that Italian company Autogrill had submitted a bid for Areas, and that around 10 private equity funds - including KKR and Lone Star - were considering making a bid.
Analysts value Areas - which has core earnings of about 200 million euros - at 7.5 to 10 times earnings before interest, tax, depreciation and amortization (EBITDA) compared to 8 to 11 times for Autogrill or Britain's SSP Group Plc.
The website for Areas says the company is France's biggest travel caterer, with 842 restaurants and outlets in France.
(Reporting by Jean-Michel Belot; Editing by Sudip Kar-Gupta/Benoit van Overstraeten)