The 18-year-old netted his first goal of the season on Tuesday night as he scored in United’s 3-0 win over Luton in the Carabao Cup.
It was his 18th goal for the club as he continues to establish himself as an important part of the first team under Solskjaer.
The Norwegian is delighted with his development, but insists he still has plenty to work on, especially his ability in the air.
The England international has largely been playing on the right of a front three for the Red Devils, and while Solskjaer sees his future down the middle, he will have to improve his heading for that to happen.
‘He can play through the middle,’ said Solskjaer. ‘As a young boy, not physically outgrown yet, sometimes it’s nice to be facing forward rather than being the number nine and being the foil and being the battering ram, if you like.
‘I scored most of my goals from just outside the posts as well, I wasn’t in the middle. For him to be a number nine, though, he needs to learn how to head a ball! I keep telling him that and if he wants to do that he’s welcome to come and practice with me!
‘He had a fantastic season last season and to get his goal now was important for him and Marcus [Rashford]. Always, for strikers to get that confidence or that feeling of scoring, to get that hunger again.
‘So very happy with that and he’ll just have to keep working to get his fitness and sharpness back as well as the rest of them.’
United travel to Brighton in the Premier League on Saturday afternoon and Greenwood, who didn’t start their opening game of the season against Crystal Palace, will likely be in the starting XI at the Amex.