However, the Red Devils may find it difficult to prise him away from the Hammers, as the club do not want to sell the Austria international and value him at £50 million, according to Sky Sports News.
The 29-year-old only joined West Ham in summer 2017 from Stoke City. He endured a tough start to the campaign but finished strongly, and he was the club's top scorer with 11 goals. He also added six assists.
Squawka Football highlighted how important he was to West Ham:
Former West Ham manager David Moyes moved Arnautovic into a centre-forward role after replacing Slaven Bilic at the helm and was rewarded as he scored vital goals that helped keep the team in the Premier League.
The Austrian's performances saw him sweep the board at the club's end-of-season awards, per Standard Sport:
Arnautovic is a real presence up front, and his aggression, strength and power make him a handful for defences. He is capable of making and scoring goals, can hold the ball up and has plenty of pace.
After proving so valuable to West Ham last season, the club would be loath to let him go. However, a huge offer for a player of his age may be worth considering, according to Jacob Steinberg at the Guardian:
Manchester United do not lack for attacking players, as they already have Alexis Sanchez, Romelu Lukaku, Marcus Rashford and Anthony Martial in the squad. However, they struggled for goals towards the end of last season when Lukaku was out injured.
The Belgian was missed, and while a Manchester United move for Arnautovic would be seen as a surprise, he could be a useful back-up to Lukaku.
Journalist Tom McDermott explained why a move to Old Trafford may not happen:
Tom McDermott @MrTomMcDermott
For those asking re this man, I think he’s had a very good season in general. Now capable of leading line and can play off front man and wide. I don’t see him starting at #MUFC though so imo and for the fee #WHUFC would want I don’t see him moving to United #Arnautovic https://t.co/nMmnmajWlO
Manchester United manager Jose Mourinho has worked with Arnautovic previously during their time together at Inter Milan.
Football writer Archie Rhind-Tutt showed Mourinho's opinion of the forward:
West Ham's price tag may be enough to put Manchester United off a move. Competition for places in the Red Devils' attack is fierce already, and £50 million is a lot to spend on a player who will not be a regular.