The defender is currently at the World Cup with France and Arsenal are looking for a new right-back following the departure of Bacary Sagna, who has joined Manchester City.
Debuchy has previously admitted he is keen to compete in the UEFA Champions League and Arsenal can offer the 28-year-old that opportunity.
However, any deal is unlikely to be concluded until after France's World Cup participation is over.
Debuchy moved to Newcastle from Lille in January 2013 for an undisclosed fee, signing a five-and-a-half-year contract.
It is understood that should Debuchy finalise his exit from St James' Park, then Manchester City's Micah Richards is on the Magpies' radar to replace him.
Richards has one year left on his current deal at City, who have told him he can leave the club this summer after he rejected the chance to extend his contract.
You can watch Arsenal in Champions League action on Sky's new home of European football, Sky Sports 5