Now, after the Austrian’s apparent transfer request, they really, really need a new striker.
With Andy Carroll and Lucas Perez already having left the club this summer, and with Arnautovic seemingly intent on following them out of the door, that leaves the Hammers with just Javier Hernandez and Jordan Hugill as senior striking options.
There are, of course, no assurances that Arnautovic will go, but given the amount of unrest he has caused at the club in recent times, it is surely time to bin him off.
And if that does happen then a replacement will be needed.
According to Football.London journalist Sam Inkersole, the Hammers could do a lot worse than AC Milan forward Andre Silva.
Writing in a piece for the outlet, he said: “The striker spent last season on loan from AC Milan at Sevilla but didn’t pull up too many trees, scoring just nine times in 27 outings for the Spanish side and a fresh start might be the perfect thing for him.
“He is expected to be put up for sale by Milan this summer, who have Krzystof Piatek as their number one striker who scores goals for fun and Silva is going to struggle for game time.
“The Portuguese frontman, still only 23 as well, could be available for a knockdown price as Milan will want to shift him on. He’s unproven in the Premier League so it would be a bit of a risk for Husillos to take.”
Inkersole is right insofar that Silva is an unproven talent in England, but that doesn’t mean he isn’t talented.
The 23-year-old already has 15 goals in 33 matches for European champions Portugal, and has the potential to keep on growing.
His time in Sevilla was hardly earth shattering, but 1.2 key passes per 90 minutes and one goal in every three La Liga appearances [Whoscored] show that there is definitely the seed of something good there.
Given the right backing, Silva could really flourish.