The 17-year-old is expected to enjoy a breakthrough season at Old Trafford after an impressive pre-season.
Solskjaer has huge hopes for Greenwood after he was asked who was the best finisher in his squad.
Firing a warning shot at both Marcus Rashford and Anthony Martial, the Norwegian responded: "They've [Martial and Rashford] still got a way to go because Mason's more of a natural finisher than them two.
"I want both of them to be more scoring easy goals because you don't have to work too hard to score them, just a little bit of movement.
"It was a great counter-attack (against Chelsea), great runs by Anthony and I think maybe he felt he should have got the first pass, it went a little bit wide out to Jesse (Lingard) and he stopped.
"But then he got himself back in a good position and even though he might have mishit it, it went in, so if you can get five extra goals like this every season, both of them, that's 10."