The Belgium international has spent the season on-loan in Germany to experience first-team football after joining Chelsea from Genk last year.
The 21-year old has impressed at the Weserstadion and Schaaf is keen to have De Bruyne at the club permanently.
"I would be kind of stupid not to want to keep such an exceptionally talented player at our club longer," Schaaf told Deutsche Pressagentur.
"Of course, we will have to wait and see what Chelsea FC intends to decide on Kevin De Bruyne's future.
"Generally, he has been a big boost for our squad. We profit because he is giving his best in the games for our club and we offer him every chance to impress while he is on loan.
"He's a great player. And Kevin told me recently how much he enjoys being at Werder Bremen.
"It's obvious that he has not yet reached his own maximum. I would be delighted to keep on working with him beyond the end of the season, that's for sure."De Bruyne has scored four goals and made five assists in 17 league games for the Bundesliga side this season.