The 23-year-old forward faces an uncertain future with the Bundesliga club as his current contract is due to expire at the end of the season.
Thuram arrived at Monchengladbach from Guingamp in the summer of 2019 and he has since made a total of 119 appearances for the German outfit across all competitions, scoring 41 goals and providing 26 assists.
The forward has enjoyed a prolific spell in front of goal so far this season, netting 13 times in 17 games, and his form was rewarded with a call-up to the France national team squad for the 2022 World Cup.
Thuram, the son of France legend Lilian Thuram, provided two assists in five substitute appearances for Les Bleus, who ultimately lost 4-2 on penalties in the final against Argentina.
Thuram is believed to have caught the eye of Erik ten Hag at Man United, with one report claiming that the Red Devils are weighing up a January move for the 6ft 4in forward.
The likes of Bayern Munich, Juventus and Inter Milan have also been credited with an interest, but German news outlet Bild claims that Newcastle are the latest club who are set to battle for his signature.
With Thuram at risk of leaving Monchengladbach for free next summer, the Bundesliga club are prepared to entertain offers of as little as €12m (£10.4m) for the Frenchman when the January transfer window opens.
Monchengladbach are also understood to have already lined up a replacement for Thuram, with Osijek striker Dion Drena Beljo said to be high on their list of targets.
Since Newcastle's Saudi-backed owner took the reins in November last year, around £200m has been spent on bolstering Eddie Howe's squad, with club-record signing Alexander Isak the standout purchase over the summer for around £63m.
Isak is one of three central striking options at Howe's disposal along with Callum Wilson and Chris Wood, while Miguel Almiron and Allan Saint-Maximin are two more attacking stars who are regarded as key players at St James' Park.
Indeed, Saint-Maximin has expressed his desire to play alongside French compatriot Thuram at Newcastle who he has known for a "long time".
"Yeah, I will be honest, I have chatted with him," Saint-Maximin told The Shields Gazette. "For me, he's a great player. I've known this guy a long time. I've been playing football with him when I was very young.
"I know all his family. He has great parents. He's an incredible guy. He is a great player and I hope we have a chance to take him here. I was so happy for him [to play at the World Cup]."
Newcastle have also been linked with a potential swoop for Barcelona attacker Memphis Depay who, like Thuram, is out of contract in June 2023.