It is understood that Chelsea were confident of signing Bournemouth frontman Callum Wilson.
That move could be accelerated now the Cherries have signed Dominic Solanke for £19million – but Merson thinks Arnautovic should be their man instead.
The Austrian has scored seven goals in Premier league 15 games this season and Merson believes £40million will convince West Ham to sell.
“Callum Wilson won’t stop Chelsea playing boring football – they need Marko Arnautovic,” Merson told the Daily Star.
“I’m not surprised Maurizio Sarri has demanded a striker this week because they need one badly and they could probably get Wilson from Bournemouth for £30m.
“He’s a willing runner and he would help them stretch the game. At the moment it’s all so slow and predictable and the whole game is being played in a 30-yard space.
“There is no movement at all and everyone just stays in their own position, so it’s easy for teams to stop and it could cost Chelsea a top-four finish.
“Wilson would help because he makes good runs and he’s scoring goals right now. Olivier Giroud is just a target man and he’s injured anyway.
“As for Alvaro Morata, I honestly don’t know what he does. I don’t know what the Spaniard gives you – and Eden Hazard is just not a striker.
“But as much as Wilson would help, I don’t think he’s the answer. He’s a good stop-gap but he’s not going to guarantee you top four.
“West Ham‘s star man Arnautovic might, though.
“He is a proven goalscorer and he gives you something different. He can make things happen and do something special.
“His agent has been making noises about him leaving as well and Chelsea could probably get him for £40m because of his age.”