The 22-year-old made his first appearance of the season in Tuesday's Champions League clash with Paris Saint-Germain, having recovered from the injury issues that had kept him out since March.
According to ESPN, United boss Ole Gunnar Solskjaer believes that the defender is capable of being a future skipper for the club, while senior figures at Old Trafford share the same opinion.
Tuanzebe, who captained United against Rochdale in the EFL Cup last September, has only made 19 first-team appearances for the club that he joined at the age of eight.
The former England Under-21 international said after the victory over PSG that United want to "dominate" in the Champions League this season. body check tags ::