The 23-year-old has made 15 appearances for the Red Devils during the 2020-21 campaign but just six of those outings have come in the Premier League.
Victor Lindelof, Harry Maguire and Eric Bailly are all ahead of Tuanzebe in the pecking order at Old Trafford, and the Englishman only has another 12 months left to run on his current contract.
According to Football Insider, Villa are keen to explore the possibility of signing the versatile defender on a permanent basis during this summer's transfer window.
The report claims that Dean Smith's side could acquire Tuanzebe for a fee in the region of £7m.
The Man United academy product has had two previous loan spells at Villa, making 35 appearances for the club in all competitions, including 30 outings during the 2018-19 campaign.