Jose Mourinho is interested in signing the 29-year-old, having briefly worked with him during his time at Inter Milan.
The Portuguese boss watched Arnautovic in action during Austrias recent friendly win against Russia and believes the Austrian would provide good back-up for Romelu Lukaku.
Arnautovic bagged 11 times in 22 games times since David Moyes appointment in December and was West Hams player of the season following his £24m arrival from Stoke last summer.
However, the Hammers are determined to hold onto their man and will demand as much as £60m from the Red Devils to let him go, according to the Mirror.
United value the 29-year-old at closer to £35m and will not meet West Hams valuation.
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If the move is to progress, the Red Devils will need Arnautovic to push for the deal and the Austrian is keen on moving to Old Trafford.
He recently admitted he was flattered by Mourinhos interest in him.
Its nice to hear, I havent heard anything from my brother, my agent, he said.
You can keep asking this question but youll never hear the answer from me.