Drogba signed a one-and-a-half-year deal when he joined Galatasaray.
That deal is set to expire at the end of the season, but the Istanbul giants will offer the 35-year-old an extension.
“Drogba has talked about issues related to the future,” Galatasaray president Unal Aysal told GSTV.
“He wants to extend his career as a player. I told him that, at Galatasaray, you can play as long as quality is evident.
“We are definitely going to offer him a [new] contract. I also do not think he will reject it.”