Thorgan Hazard was on Chelsea's books between 2012 and 2015, but failed to force his way into the first team, unlike his older brother, who remains one of the club's best players.
Hazard Jr spent much of his Stamford Bridge career out on loan, before joining Borussia Monchengladbach permanently in 2015.
The 24-year-old has flourished in the Bundesliga, becoming one of the German top-flight's most feared attacking midfielders.
The Belgian has scored seven goals and laid on a further seven assists in 20 appearances in all competitions so far this season, with English publication 'The Daily Mail' claiming that Conte is considering a move for the former Chelsea man off the back of his impressive form.
Hazard was recently asked by German newspaper 'Bild' about rumours over his future but he refused to be drawn, simply saying: ‘If you play well in your club and help your team win, that makes one of course interesting for big clubs.
'At the moment, only Borussia counts for me. And that the club will qualify for Europe again.’
Should Chelsea make a move for Thorgan, he would become the third Hazard brother at the club, with the youngest member of the Hazard clan, Kylian, having also joined the 'Blues' last summer.