Defender Tuanzebe departs United during an uncertain period ahead of the transfer window closing on Thursday, with Jose Mourinho's side attempting to bring in a centre-back before the deadline.
The 20-year-old spent last season on loan at Villa, though he played in just five games in the Championship.
Tuanzebe has made eight appearances for United in total since his debut back in 2017, but was a regular for the club's Under-23 side last term.
Jose Mourinho has repeatedly expressed his frustrations at his side's failure to bring in new players in the transfer market, with only Fred, full-back Diogo Dalot and goalkeeper Lee Grant arriving thus far.
It remains to be seen if United will make any new additions, with time running out for the club ahead of the Premier League transfer deadline at 17.00 BST on August 9.