According to 'Bild', the clause expires on 31 December 2016.
Hazard has impressed at Borussia Monchegladbach since joining the club initially on loan in 2014.
The Belgian has played 87 times for the Bundesliga side and scored 18 goals, one of which came against Barcelona in the Champions League on Wednesday evening.
The 23-year-old failed to make a single appearance for Chelsea's first team when at Stamford Bridge, but the Blues said that they would "monitor his progress" in Germany.
However, Eden's younger brother claims he is "only focused" on his current club.
"I've signed a long-term deal and I am only focused on Borussia," he told 'Bild'.
"I feel good here, and am currently not thinking about any other club".