The 26-year-old, who has started just eight Bundesliga games this season, claimed in an interview with German publication Bild that he felt unsettled at the Allianz Arena.
Costa also suggested that teams from the Premier League, La Liga, Ligue 1 and the Chinese Super League had made contact over a move away from Bavaria, but Ancelotti is adamant that the Brazil international - the scorer of four goals last season - is going nowhere.
"I didn't read the interview, but I speak to him regularly, he is satisfied to be here," the former Real Madrid boss told reporters. "When it comes to the happiness or the sadness of the player, there are agents who maybe want to put pressure on the club, who want to be more involved.
"I have a direct relationship with the player. He's happy to stay here, he is involved and that counts for me. I think the interview came more from the agent than from the player."
Costa has featured in every game for Bayern since the 4-1 win over PSV Eindhoven in mid-October.