The France full back has been a consistent performer for Alan Pardew’s side this season, and has caught the attention of Roma boss Rudi Garcia.
The pair previously worked together at Lille, and enjoyed success winning a league and cup double in 2011.
Both could be keen on a reunion, with Roma riding high in second place in Serie A and on course for Champions League football next season.
Debuchy has been a regular at St James’ Park since his switch in January 2013, clocking up 39 Premier League appearances so far.
He is under contract at St James’ Park until 2018, and would demand a fee of at least £8.5million.
German giants Bayern Munich are also understood to be trailing the Frenchman, but Roma remain the favourites for his signature.
Should Debuchy complete the switch to Rome, he will be reunited with former Lille teammate and Arsenal forward Gervinho, who has enjoyed a new lease of life in Serie A after two poor seasons in front of goal at the Emirates.