The Hammers are very unlikely to be willing to part ways with the Austria international, and are reportedly putting a £50million price tag on Arnautovic.
The 29-year-old joined the London outfit from Stoke City last summer, and despite struggling through a less than impressive first half, rounded off his season having scored 11 goals since December.
Arnautovic has previously worked with United boss Jose Mourinho at Inter Milan back in 2009 and reportedly found a somewhat kindred spirit in the Portuguese.
Manchester's interest may be deterred a little given that the Austrian has four years left on his contract with West Ham, but Mourinho's side are desperately seeking to firm up their attacking options ahead of next season.