The 33-year-old former Stoke and West Ham forward was linked with Manchester United over the weekend, and reportedly his Italian club turned down a low ball offer for him.
United have also been linked with Juventus midfielder Adrien Rabiot who, like Arnautovic, comes with a bit of baggage.
Arnautovic scored 43 goals in 184 Premier League games at Stoke and West Ham before leaving for China in 2019. He is currently at Serie A side Bologna, where he scored 14 goals in 33 appearances last season.
Speaking on BBC Radio 5 Live's Monday Night Club, pundit Chris Sutton said: "That's madness, thinking about signing Arnautovic.
"I thought it was a spoof, it's ridiculous.
"It's a real wrong move in terms of the eyes of the supporters. There's a million other players out there United should have been linked with. I do no get that.
"It's an absolute PR disaster. If Arnautovic comes in, that's going to put Ten Hag under so much pressure."
Meanwhile on Sky Sports Gary Neville was so unhappy about the move he didn't have an opinion, which is very rare.
"I don't even want to comment on Manchester United signing Marko Arnautovic."