The 24-year-old is undeniably gifted – so talented that Inter Milan brought him in for the 2009-10 season.
But the 6’3” forward has the “attitude of a child”, according to Chelsea boss Jose Mourinho, who signed him for the Italian giants before washing his hands of the problematic player.
Where do we start? While still at FC Twente in Holland – where he came through the youth ranks – Arnautovic had a reputation for being juvenile and a poor trainer. No drinking, no clubbing, and totally dedicated to football – but petulant and rebellious.
The spotlight is less bright in the Eredivisie though, so he was able to become a first-team player before Inter took a punt on him.
Even back in 2009 though the Nerazzurri were reluctant to sign him permanently, electing for a loan deal so they could check him out.
While it is unclear exactly what he got up to in Milan, the Special One said he was "a fantastic person but has the attitude of a child".
Needless to say, he became close with Mario Balotelli, whose behaviour also infuriated Mourinho but who has a slightly more professional demeanour.
It wasn’t just any old match too – Balotelli and Inter had just won the Champions League.
A move to Bremen followed, where he almost immediately irritated his senior colleagues, with Torsten Frings branding him "arrogant".
He has been repeatedly kicked out of the Austria squad for misbehaving, has been done for speeding and had '2010 Champions League winner' embroidered on his boots when he barely played that season and wasn’t even on the bench for the final.
Arnautovic also has a prickly relationship with the media – the early pranks and jokes have subsided and he now barely gives interviews for fear of getting in trouble.
Our colleagues in Germany know him best though, so they compiled a rap-sheet for the man who once described Balotelli as an "angel"…
- Public dispute with former Werder director Klaus Allofs (October 2010)
- Dressing room fight with Austria striker Stefan Maierhofer during Euro qualifier (March 2011)
- Despite not being much of a party animal, managed to get suspended by Bremen for going clubbing before a match. Also suspended by country (May 2011)
- Tore knee ligament playing with dog. Out for two months (March 2012)
- Insulted a policeman during a routine traffic stop in Vienna: "Shut up. I earn so much money, I could buy your life" he said. (June 2012). Apologised afterwards.
- Incurs wrath of Austria fans for glaring miss in match with rivals Germany (September 2012)
- With team-mate Eljero Elia, stopped for driving with excessive speed on the Autobahn late at night, 36 hours before kick-off against Leverkusen. Suspended by club and country (April 2013)
- Fought with team-mate Sokratis (April 2013)
- Sold to Stoke (September 2013)
Eurosport Germany’s Daniel Rathjen said:
Othmar Larisch discovered his talent in Vienna and once said about him: "He has a problem with his head, otherwise he wouldn't act like that. He has inferiority complexes and should go to a psychologist. That would help him very much."
His football skills are still extraordinary, but at Bremen he got a lot of chances before they finally lost patience and let him go.
If he doesn't change his behaviour and the British press writes only bad news about him like in Germany and Austria, he will fail at Stoke again.
By Reda Maher / On Twitter @Reda_Eurosport