Jorginho — a Brazil-born Italy international — could be a perfect fit for United, who want to strengthen in that area, and his representatives reportedly made a trip to Manchester last month.
The player's agent, Joao Santos, said: "I think we'll discuss a renewal at the end of the season, as it's not the moment to talk about that, because he still has a long contract.
"He wants to stay, although we'll have to see if Napoli agree with that. If a player like (Lucas) Torreira arrives from Sampdoria, then that will require an important investment and Jorginho could be sacrificed to make way.
"I think they'd rather sell Jorginho than Amadou Diawara, who is younger.
"It's an issue of mentality, it's a family at Napoli and they all play for each other. Right now everyone is concentrated on the Scudetto, an objective they've been missing.
"He has been there for four years now and feels Neapolitan."