Sky Sports News say the understand the Hammers have no intention of the selling the 29-year-old and value him at £50m.
Arnautovic joined West Ham from Stoke for a club-record £24m fee last summer and scored 11 goals during his debut season with the club and was voted Hammer of the year.
The story first emerged five days ago on website Arab news. They quoted sources close to the United manager who said Arnautovic has impressed Mourinho during the campaign in which he often operated as a solo striker
Claret and Hugh will attempt to find out whether there is any substance to this latest doubtful transfer rumour.