Fellaini followed David Moyes from Everton to Old Trafford last summer but the Belgian has failed to settle at United, who are understood to be willing to cut their losses on the £27million midfielder.
Napoli boss Rafa Benitez is said to be keen on bringing Fellaini to Serie A, with the player also understood to be enthusiastic about linking up with the former Liverpool and Inter Milan coach. Fellaini's agent has denied reports of a meeting over the weekend between Napoli and the 26-year-old, but Italian newspaper Corriere Dello Sport claims that there is a willingness from all sides to reach an agreement.
United would rather sanction a cash deal and will consider offers in the region of £15million, but Napoli are understood to prefer an initial loan move, with a small fee and the view to a permanent transfer.
Fellaini's wages could also be a sticking point, with the Belgium international said to earn in excess of £100,000-per-week and four years still remaining on his contract at Old Trafford. Napoli admitted earlier this summer that they could not afford to make Pepe Reina a permanent signing due to the goalkeeper's salary at Liverpool. The Spaniard has returned to Anfield after spending last season on loan in Naples.
But Louis van Gaal is said to have told United executives that he does not see a place for Fellaini in his ranks, having already spoken of the excess of attacking midfielders in his "unbalanced" squad. Fellaini reported back to Manchester this week for pre-season training after the World Cup, but it would appear unlikely that he will still be there by the end of the transfer window.