The 25-year-old, who is the son of France legend Lillian Thuram, has been in sensational form for the Foals this season.
Thuram, who is with France at the 2022 World Cup in Qatar, has scored a staggering 13 goals in only 17 appearances across all competitions, while also providing four assists for the German club.
However, Monchengladbach appear to be open to the option of selling him in January due to his contract expiring at the end of the season, when he will be able to leave as a free agent.
"There may be changes in winter, but it may also be the case that there aren't any," Gladbach sporting director Roland Virkus said when asked about the January window in general.
"Of course we're in talks with the players. I can't tell you right now whether these players will still play here after the winter or in the coming season."
Thuram signed for Gladbach in 2019 from French side Guingamp for around €12million, and his current employer may be looking to recoup some of that during the winter break.
Bayern Munich, Inter Milan, and Atletico Madrid have been touted as potential destinations for the talented attacker.