The Austria international, who has four years remaining on his Hammers contract, insisted that he is happy at the London Stadium and has had no contact with United.
"I am happy with my job. Whatever happens will happen. I've never heard anything," Arnautovic told Sky Sports News.
"Even three weeks ago I haven't heard anything. That's why I cannot say anything about it.The only thing that bothers me is that I am in good health and that I am able to play football.
"I have a contract at West Ham - that's all we have to talk about."
Arnautovic joined West Ham from Stoke City last summer in a club record-club £25m deal.