The versatile defender has not played a competitive match since last December but is now looking set to stake his claim for a starting spot later this month.
Tuanzebe has missed the start of this season due to a foot injury and was wearing a protective boot during the summer.
That came off at the start of this campaign and he has now resumed full training with the hopes of breaking into Solskjaer’s plans.
He is potentially in line for a return for the Premier League trip to Newcastle on October 17, according to the Telegraph.
Tuanzebe, 22, featured 10 times for the club last season, but didn’t play after Christmas due to injury.
His return could provide a timely boost for Solskjaer as he looks to fix his leaky defence.
Harry Maguire and Victor Lindelof have both been guilty of errors in the opening matches of the season, while Eric Bailly’s return to the backline did little to improve matters in a 6-1 thumping at the hands of Tottenham Hotspur.
Solskjaer rates Tuanzebe highly and appreciates his ability to play across the back-four, while he can also drop in at the base of midfield.
The Manchester United manager could be set to shuffle his pack at the back, with Marcos Rojo, Timothy Fosu-Mensah and Phil Jones also in contention for centre-back spots, while the arrival of Alex Telles provides a fresh option at left-back.
Tuanzebe’s fellow academy graduate Teden Mengi, 18, is also well thought of by Manchester United’s backroom staff and is viewed as a future first-team player.