Red Devils manager David Moyes is expected to delve into the January transfer market in the coming weeks, with a new midfielder having been made a priority after a disappointing start to the season at Old Trafford.
Hamsik has emerged as a target, with the Slovakian international having been one of Serie A’s top performers for some time.
Moyes is thought to see the attack-minded ace as the sort of player that could inject some guile and determination into his engine room, which has been severely lacking in dynamism so far this term.
Despite being one of Napoli’s star men, the Italian side are believed to be willing to listen to big offers for the 26-year-old.
Paris Saint-Germain are also in the race but United may look to beat the Ligue 1 champions with a £25m offer.
However, Hamsik may have reservations about joining Moyes’ side, with Champions League qualification for next season far from a certainty.
The rampaging midfielder also only signed a new contract over the summer, which indicates that he is settled in Naples.