Lille coach Rudy Garcia claims Newcastle have offered the figure, which he clearly considers derisory.
Speaking to French website 20 Minutes, Garcia said: "I believe Newcastle have faxed an offer of £4million - but they have the wrong player!"
The 26-year-old, with seven caps to his name overall under France coach Laurent Blanc, has so far impressed in Euro 2012 in Group D games with England and Ukraine.
Garcia, however, believes Debuchy could move on this summer after nine years and over 200 Ligue One appearances for the club.
With Inter Milan also rumoured to be interested, Garcia added: "He is torn between staying with us and playing in the Champions League in our new stadium or going elsewhere.
"If he does go and it is a sporting progression, then we will be happy to see him evolve - but we have not planned to replace him."