According to French journalist Cédric Rablat of Foot Mercato, the Clarets have put in the bid for the 26-year-old, an international teammate of Maxwel Cornet, although he is currently not on duty at the Africa Cup of Nations.
Suggestions are that it will take more than than offer to persuade Lens to sell the former Manchester City youngster, who also had a spell with Fulham.
Fofana started out with Paris FC, joining when he was nine, before a move to Lorient aged 17.
Two years late who joined City's development squad, and scored five goals in 20 appearances for the Under 18s in 2013-14, as well as two in seven games in the UEFA Youth League under Patrick Vieira.
In November 2014, he joined Fulham for two months, and extended the deal to the summer, making 25 appearances in the Championship.
That summer, he went back to France on loan at Bastia, and in 2016 he joined Udinese for £2.5 million.
After two years in Italy, he joined Lens, signing a four-year deal to 2024.
After playing for France at U16, U17, U18 and U19 level, in 2017, he opted to represent Ivory Coast, where his parents hail from, and made his debut in a World Cup qualifier against Morocco.