The 27-year-old has been linked with a move to the Premier League for over a year now and he was reportedly close to joining Everton last August.
That deal, however, ending up collapsing and the Algerian has more recently been on Marseille's radar.
The French club are fans of Abdennour and manager Rudi Garcia is eager to take him to the Stade Velodrome this summer.
However, according to Foot Mercato, Marseille will have to fend off competition from both Leicester and Southampton if they want to land the centre-back.
The Premier League duo are said to be tracking Abdennour and they are prepared to make formal offers if he becomes available.