The 28-year-old joined the Red Devils following a highly-anticipated switch from Ligue 1 club Monaco in the summer of 2015, and has since scored 90 goals in over 300 appearances.
Martial was sent out on loan to Sevilla for the second part of the 2021-22 term as he searched for regular first-team minutes, however the Frenchman has been back at Old Trafford since June 2022.
The former Lyon youngster has appeared in 13 Premier League matches for Erik ten Hag's men so far this campaign - earning only five starts - finding the net during the 3-0 win over Everton at Goodison Park on November 26.
According to Italian outlet FC Inter News, last season's Champions League finalists Inter Milan are keen on bringing Man United's Martial to Serie A in the New Year.
The report claims that the Nerazzurri are big admirers of the attacker and would be willing to bring him to the San Siro to provide support for 14-goal forward Lautaro Martinez.
Martial has left six months left on his current deal at Old Trafford, although the Red Devils possess the option to extend the agreement by a further 12 months.
Despite this, Man United are understood to have no desire to stretch the forward's stay at the club past the conclusion of the 2023-24 campaign.
The Frenchman's playing time on the red side of Manchester has been limited by the arrival of Rasmus Hojlund from Atalanta BC for £72m in the summer.
The Dane is yet to score in 12 league appearances for Ten Hag's side but was useful in the Champions League group stage, making the net ripple on five occasions in six matches.
It is believed that Saudi Pro League side Al Ettifaq are also interested in signing Martial during the January window, with the Middle East club prepared to pay £8.6m for his services.
Ettifaq are currently under the management of Liverpool legend Steven Gerrard, who has already lured former Reds Georginio Wijnaldum and Jordan Henderson to Prince Mohamed bin Fahd Stadium.
Martial is said to be a player who United will entertain offers for in the New Year, so the attacker's eight-year association with the Red Devils could be coming to an end in the near future.
Both Marcus Rashford and the 28-year-old missed Man United's crucial continental clash with Bayern Munich on Tuesday due to illness, however both are targeting returns as the 20-time English champions travel to Jurgen Klopp's Liverpool on Sunday afternoon.