The in-demand Fenerbahce defender has been a star in the Turkish Super League since arriving from Lille back in 2015.
Both Chelsea and Manchester United have been linked with summer moves for the 28-year-old but now, according to reports in Turkey, Marseille are at the front of the queue.
Boss Rudi Garcia worked alongside Kjaer at Roma, which could be detrimental to the Premier League duo's hopes of landing the defender.
Fenerbahce may be forced into selling their star asset at the end of the season if they miss out on Champions League football.