Right-back Debuchy, 26, has informed the club he is ready to move on to pastures new, with Inter Milan also tracking his services.
Lille's assistant director general Frederic Paquet: "For a player to leave, there are two conditions which have to be met.
"First, we need to have a replacement. Then we will see if the offer lives up to what we expect.
"Mathieu clearly has no substitute, although we are looking. We have heard that he wants to leave, but as we speak there is no replacement.
"We have received an offer, but it was not what we are looking for."