Sport-Bild claim the Blues are considering the Belgian forward again - two-and-a-half years after they sold the younger brother of Eden to the Bundesliga club for a reported fee of £6million.
Chelsea wisely inserted a clause in that deal which gives them first refusal on Hazard if they match any bid deemed acceptable by Borussia.
The 24-year-old is understood to be attracting interest from bigger clubs after seven goals and seven assists in 20 Bundesliga matches this term.
Gladbach manager Max Eberl admits he would first have to inform the Chelsea hierarchy of any bids - who could then decide whether to submit their own offer. "We do not need to make any secrets about it - if we get such a player from Chelsea, then Chelsea naturally has the ability, in whatever form, to think about this player," said Eberl.
Hazard, speaking when he made the move in 2015, said: "I am focusing on excelling at Borussia Monchengladbach, but I still hope to play for Chelsea one day."