The 23-year-old midfielder is under contract with Rennes until the summer of 2017, but all three Premier League sides are hoping to bring him to the Premier League this month.
It is claimed that Watford made an offer of roughly £7.3 million towards the end of the summer transfer window, but no deal could be finalised before the window closed.
However, the Hornets retain their interest in Doucoure, and they have made an enquiry to Rennes ahead of making another approach for the former French Under-21 international this month.
Newcastle and Leicester have also made enquiries for Doucoure, who has played 13 games in Ligue 1 this season, scoring two goals and registering two assists.
A central midfielder, Doucoure is well regarded for both his attacking and defensive play, although he has spent much of this season playing in a more advanced role.
He has alternated between featuring as a number 10 and a right winger, whilst he has also played as a striker on occasion. However, his more natural role is slightly deeper, and he can play in a holding role as well if needed.
There are no indications that any formal bids have been made for Doucoure, but it is clear that the trio of Newcastle, Leicester and Watford want to bring him to England before the end of January.