Debuchy has emerged as the Magpies' preferred replacement for right-back Danny Simpson, who is expected to leave St James' Park this summer unless he is able to agree a new deal.
Even if Simpson remains on Tyneside, Alan Pardew is keen to strengthen his back four and Debuchy would still be a desirable option after an impressive campaign in Ligue One.
The 26-year-old is a close friend of Newcastle midfielder Yohan Cabaye and has expressed a desire to move to the Premier League once he has represented France in the European Championships.
Lille boss Rudi Garcia: "I want all the important players to stay at Lille next season.
"I include Mathieu in that.
"I want him to have a great time at the Euros and then come back to us and show his best form during the summer."
As well as targeting a full-back, the Magpies manager is also keen to recruit a new centre-half, with the likes of Jan Vertonghen, Douglas and Mapou Yanga-Mbiwa under consideration.