The Belgian winger was taken to Stamford Bridge last summer, but immediately allowed to head to Germany.
The 21-year-old has impressed during his time in the Bundesliga, with Bayer Leverkusen and Wolfsburg also believed to be closely monitoring his situation.
Werder hope they have put themselves in pole position should there be the possibility of doing a deal, with it unclear where De Bruyne stands in England.
He is yet to make a competitive appearance for Chelsea, but the Blues are well-stocked for midfield options and he would appear to be some way down their playmaking pecking order.
Werder would welcome the opportunity to move to the negotiating table, with sporting director Thomas Eichin of the opinion that De Bruyne's career would benefit from an extended spell at his club.
He said: "We have made no secret of our interest in keeping Kevin.
"We are the right club to advance his development."