The 25-year-old had appeared to be on the verge of moving to Liverpool back in the summer but his club Lyon pulled out of the deal at the last minute.
Liverpool are reported to be still interested in the France international, however, it is now Chelsea that is seen as the firm favourites to land the versatile forward.
The reports also claim that the Blues have already made contact with the player through his agent Pini Zahavi.
No deal is expected to be completed in the winter and a summer signing looks far more likely, though Chelsea are keen to avoid any delays that allows the door to be reopened for Liverpool.
What is almost certain is that Fekir will be playing in the Premier League next season, whether it is Chelsea or Liverpool is open to debate but as things stand right now it is Chelsea that appears to be the front-runners.