“I’d take him in a heartbeat. I think he’d fit perfectly into Chelsea."
Cascarino believes Arnautovic's maverick personality could be of huge benefit to Chelsea, who have been unable to find consistency in recent weeks.
Their 1-0 home defeat by Leicester on Saturday means they are almost certainly out of the running for the Premier League title.
And Cascarino thinks Arnautovic could come in and give them a lift like Eric Cantona did for Manchester United when he moved during the 1992/93 season and inspired them to a first league title in 26 years.
Gonzalo Higuain has been linked with a move to Chelsea (Image: GETTY)
Olivier Giroud has struggled for goals this season (Image: GETTY)
“The thing with Arnautovic – he reminds me of that Eric Cantona mindset,” he added.
“He thinks he’s good enough to be up there at the top table, and he is.
“He was dreadful at times last year, but there’s a real player in there and he needs a challenge.
“And maybe the challenge is West Ham? I’m not saying he should leave West Ham, but he is a guy who needs to be winning things.
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Alvaro Morata is also misfiring (Image: GETTY)
“He’s that good of a player.
“Arnautovic is a player capable of playing for one of the best teams in England.”
The Austrian has scored five Premier League goals in 13 appearances this season and laid another two assists.
He was the Hammers’ top scorer last season after striking 11 times as he made the switch from winger tocentre-forward.