Arnautovic only joined West Ham from Stoke City last summer in a club-record deal worth £24m and tallied 11 goals and six assists in his first year at the London Stadium.
The 29-year-old is a natural left winger, but can play on either side of the attack and was utilised as a striker by manager David Moyes for the latter stages of the 2017-18 season.
According to Sky Sports News, Arnautovic is considered to be in new manager Manuel Pellegrini’s plans for the upcoming campaign, and therefore not for sale, and is likely to cost at least £50m.
He arrived in the Premier League in 2013 after moving to Stoke from Werder Bremen and has since grown his reputation as a powerful forward who is strong with both of his feet.
Arnuatovic made his debut for the Austrian national team in October 2008 and has earnt 69 caps since, scoring 19 goals and making 16, and would surely be interested in a move to Old Trafford if approached.
Mourinho is also said to be interested in Chelsea’s Willian and Real Madrid’s Gareth Bale as he searches for a first-choice right winger, which could make the potential capture of Arnautovic slightly underwhelming amongst Man United fans.