The young centre-back returned to United this summer after a season long loan at Aston Villa.
After helping the Villains to promotion, Tuanzebe got his chance to show Solskjaer what he could do during preseason.
His performances earned him a spot on the bench for their first Premier League game of the season against Chelsea last weekend.
"Pre-season was a great chance for Axel to show what he's capable of next to our players," Solskjaer said about the young defender to reporters.
"I've seen him at Villa, I've seen him in midfield here, and at right-back. But I wanted to see him next to Victor, next to Phil.
"We know he's going to be a big, big part of this club in the future.
"He probably impressed me more than I expected. That's why he's on the bench.
"He can slot in midfield and right back as well, so he's able to play different positions."