The 29-year-old played with Crocuhh during their time together at Stoke City, before joining the Hammers in the summer of 2017, for a fee believed to be worth somewhere in the region of £20 million.
Arnie's future at the London Stadium is far from certain, however.
There has been interest in his signature from China this week, with various media outlets reporting a bid of around £35 million for the West Ham man's services.
The Austrian's brother and agent then suggested that his clients wants to leave east London, before being quickly shot down by the club's hierarchy, who suggested that he is not for sale for any price.
Crouch explained how Arnautovic has the ability to be a success at the very highest level in the game, however, when speaking exclusively to the Daily Mail:
"Marko Arnautovic always struck me as a player who could end up at Manchester United, and Old Trafford looked like it would be the perfect stage for him. Some of you may laugh at that statement but, believe me, Marko has always had special ability."
Whether United make a late play for Arnautovic remains to be seen, but whatever happens, West Ham must do all that they can to keep hold of the 29-year-old.
If they are to have any chance whatsoever of finishing inside the top seven this season, they will certainly need the Austria international on board.