21-year-old Hazard, brother of Eden, joined Chelsea in 2012 from Lens, but has spent the last two seasons on loan at Zulte Waregem.
Hazard impressed with Zulte, winning Player of the Year in Belgium and also becoming a full international.
He has been linked with a possible move to a Premier League club, but he looks to be heading to the Bundesliga with Schalke, Wolfsburg and Monchengladbach all linked.
It is Monchengladbach who claim to have landed him, with sporting director Max Eberl telling the Rheinischen Post: "We were always going to make an attacking signing, no matter what the situation is with Luuk de Jong and Peniel Mlapa, and this will be Thorgan Hazard.
"We have exchanged contracts with Chelsea and we have agreed with Thorgan, we have all agreed and now just need to sign the contracts."