The former Jimmy Murphy Youth-Team Player of the Year spent last season on loan at Aston Villa and has returned to the Reds this summer, playing in the victory over Perth Glory.
On Saturday, Tuanzebe was named in a strong starting XI against Inter in Singapore alongside Victor Lindelof and he played admirably, handling a physical and competitive Italian side with confidence.
Axel will have gained plenty of match sharpness and fitness from his 61-minute outing against Antonio Conte's Inter.
In the post-match press conference at the Singapore National Stadium, Solskjaer was asked for his opinion on the 21-year-old and whether he had decided his future for the imminent 2019/20 campaign.