The Ghanaian hasn't had the easiest start to the season and a January move to the Bundesliga has been suggested.
"I've heard the story that I'm off to Bayern, but there is no truth in that," the attacking midfielder said. "It's just a rumour.
"I can say something very clearly and that is that I am happy at Milan and I am not ready to leave this club.
"I owe a lot to Milan and I'm not thinking about Bayern Munich or any other team."