The France winger joined the Bavarians on loan from Juventus in 2015 on a two-year deal, with the option to sign him permanently for 21m euros at the end of the current campaign.
Rumours have been rife about his future in recent weeks, with a number of English clubs linked with potential swoops if he becomes available.
A lack of game time this season under Ancelotti has led to suggestions he is unhappy at the Allianz Arena but the Italian has now allayed fears he could leave.
The coach says the 20-year-old's limited opportunities have mainly been down to his fitness worries and has revealed they have every intention of signing him permanently in the summer.
"He has had a lot of problems, but now he is fit and in good shape," he told reporters. "The idea is that he stays here next season."