Reports had claimed that United boss Jose Mourinho had personally been to watch Arnautovic in action when Austria defeated Russia in a friendly last week, with a view to a summer move for the 29-year-old.
Mourinho worked with Arnautovic during his time at Inter Milan and was reportedly keen on a reunion at Old Trafford.
However, speaking to 'Sky Austria', Arnautovic himself poured cold water on the reports, saying: "I am happy with my job. Whatever happens will happen. I've never heard anything.
"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 got his West Ham career off to an inauspicious start after being sent off in only his second game for the club, as well as going 11 games without a goal.
However, a run of five in five followed, allowing the Austrian international to finish the season with a respectable total of 11 goals and eight assists in 35 games in all competitions.