Thuram will be leaving Gladbach at the end of the season on a free transfer and several clubs are interested in getting their hands on him.
He has scored 16 goals in all competitions this season and his free-agent status has made him a big target for several clubs across Europe.
Chelsea have long been interested in him and have been pushing to take him to Stamford Bridge this summer.
But according to French sports daily L’Equipe, the striker has knocked back a massive contract offer from the Blues.
Thuram is not keen on a move to Chelsea given the turmoil the club have been going through this season.
The forward wants a more stable environment and is also keen to play in the Champions League next season.
Manchester United remain interested in him but a move for Thuram is hinging on the club’s takeover process.
The Frenchman also has concrete offers on his table from Atletico Madrid and Inter ahead of the summer.