Baba Rahman joined Schalke last summer on a season-long loan move from Chelsea, and the Bundesliga club want to make the deal permanent, according to German outlet Fussball Transfers.
The 22-year-old played only one game at the African Cup of Nations with his national team Ghana, before suffering a serious knee injury.
Schalke sporting director Christian Heidel said: “We’ve really missed him after his cruciate and meniscus injury, which he has suffered during an assignment with Ghana at the Africa Cup.
“But that’s why we do not ignore him. If it is possible, we would like to keep him.
“I do not think it’s impossible for him to play next season for Schalke.
“Of course, his home club Chelsea plays the decisive role.”