The Hammers boss said: “I cannot tell everyone what they must say or what they must not say. Everyone is the owner of their own words.
“Marko can say what he wants. But he is a West Ham player because he has a contract here. He is happy here.
“Every player always wants to play in the biggest team.
“But I don’t think that Marko is thinking about that, he is thinking about West Ham and he tries to make his best performance in every game.
“I expect him to give his maximum performance in every game. He has a lot of power and scores goals. I expect him to do a complete season in the way he did for half a season last year.”
Arnautovic, took four months to score his first goal for West Ham last season before ending the campaign with 11.
He already has five so far this season despite being limited by a knee injury.