Tuanzebe, 22, was named in a matchday squad for the first time at the age of 17 by Louis van Gaal in October 2015 but has only started 12 times for United.
The academy graduate missed four months of the 2015-16 campaign and was sidelined by hip, hamstring and foot injuries last term. Tuanzebe also fractured his metatarsal whilst on loan at Aston Villa in 2018.
Jose Mourinho gave Tuanzebe his United debut in January 2017 and he was entrusted to start the final four Premier League games of 2016-17 but has only lined up twice in the league under Solskjaer.
Harry Maguire could be fit to play against Chelsea on Saturday, leaving Solskjaer with the dilemma over whether to drop Tuanzebe after his stunning return at Paris Saint-Germain in midweek.
“We’ve always known Axel is a very good centre-back and if he keeps fit and stays fit he’ll play a lot of games for us,” Solskjaer said. “He’s got all the attributes a centre-back at Man United needs. He can play right-back and centre-mid. He played left-back last season against Arsenal, he played a fantastic game apart from one pass – a square pass.
“For me now, it’s about keeping him injury-free, keeping him consistently out there on the training ground and playing games so he’s got all the work, because he’s missed too much football early on in his career.
“We knew he was due to be fit around about this time and he’s worked really hard. We believe in the kid, that’s for sure. He’s proven that in glimpses but now it’s about being consistent.”