However, they claim that the bid has been rejected and Leicester will follow up with an improved offer in the coming days. RMC report that Leicester manager Claude Puel is an admirer of the player.
Who is Bouna Sarr?
Sarr, 25, scored seven goals in 92 league appearances for Metz between 2011 and 2015 before earning his move to Marseille.
The right-winger, also capable of playing at right-back, is a Guinea international and has made 19 appearances for Marseille so far this campaign, including six in the UEFA Europa League.
History could repeat itself
Leicester have had previous success when entering the French market for wingers. They signed Anthony Knockaert - a key member of the Championship winning squad - from Guingamp for a fee in the region of £800,000.
They followed this up with the signing of Algerian winger Riyad Mahrez, who joined from Le Havre for around £400,000.
Most recently, Leicester signed Malian winger Fousseni Diabaté from Ligue 2 side Gazélec Ajaccio. Diabaté signed a four-and-a-half year deal with the Foxes and travelled with the squad for last weekend's 0-0 draw against Chelsea at Stamford Bridge.
Scuppering another potential move?
If Leicester were to sign Sarr, it could cast doubt over any potential move for Paris Saint-Germain outcast Hatem Ben Arfa.
Ben Arfa's contract expires this summer, and with Puel getting the best out of the French winger during their time together at Nice, various media outlets have reported Leicester's potential interest in the former Newcastle United and Hull City winger. However, if Riyad Mahrez stays at the club - and the Foxes sign Sarr - it would be very difficult to see how Ben Arfa would fit into the side.