The newspaper claim in their live transfer blog [08:30] that the club have rejected a £35million offer from China for the Austria international, whose agent has claimed he wants to leave.
The Mail report that the Hammers could be tempted into selling their prized asset if a bid close to £50million was made, with the unnamed Chinese club set to improve their bid while offering Arnautovic wages of £200,000-a-week.
Good move for West Ham?
If they were to receive £50million, then it is hard to say no.
The Hammers paid Stoke £20million-plus for Arnautovic in the summer of 2017, and the Austria international has been a brilliant servant so far.
His goals have carried the club at times since his arrival, and losing him would be a blow, but recouping £50million for a player who is almost 30 is too good to turn down.
That would give Manuel Pellegrini the chance to reinvest some of that money into more players he wants as he tries to plug some gaps in his squad.
This is Futbol rating: 7/10
Likely to happen?
It says that a fresh, improved bid is on the way for Arnautovic, but it is doubtful that this unnamed club will bid £50million for the 29-year-old.
Obviously we will have to wait and see, but the likeliest outcome this month remains Arnautovic staying at the London Stadium until the summer.
This is Futbol rating: 2/10