The 17-year-old scored his first senior goal for United in their 4-0 pre-season thrashing of Leeds in Perth on Wednesday.
Solskjaer believes the goal will have lifted the pressure off Greenwood’s “talented” shoulders and has challenged the United academy prospect to push on and fulfil his potential.
“We were delighted with the goal he scores, it’s important for strikers to get that goal,” Solskjaer told his post-match press conference.
“We’ve said and know he is capable of scoring goals, but that first one maybe takes a weight off his shoulders. His movement, cleverness – the young boy is going to be a very good player.
“He can play in all of the front four positions, he’s a natural footballer. He’s good coming in on his left foot but he can play anywhere along the front line.
“He’s a talented boy and has every opportunity to make it as a Manchester United player. If he stays clear of injuries and stays professional, I’m sure he is going to take his chance because everything is there for him.”
Asked if Greenwood would be in contention for United’s first game of the season against Chelsea on Super Sunday on August 11 – live on Sky Sports – Solskjaer added: “He has got a chance to start that one, definitely.
“He is more than capable and will always be there in and around the box creating chances. I won’t say that it is not a possibility, there’s a good possibility if he keeps going as he is. It’s difficult to keep players out that perform well.”
Solskjaer’s rising stars
Sky Sports reporter Jack Wilkinson: “Greenwood wasn’t the only United youngster to catch the eye in Perth, there was talent all over the pitch – how many times have we been able to say that in recent years?
“Summer signings Aaron Wan-Bissaka and Daniel James, both aged 21, got valuable minutes under their belts ahead of their first season at United, with James denied his first goal for the club by the post at the end of the first half.
“After the break, Tahith Chong and Angel Gomes, both aged 18, tormented the leggy Leeds defence with a series intricate attacking moves which oozed with complexity and success, eventually leading to United winning their penalty.
“This wasn’t showboating, far from it, this was effective attacking flare, the like rarely seen in such abundance at United in recent years.
“What’s clear as United leave Perth for Singapore is that the younger players at Solskjaer’s disposal are eager to put his methods into practice with a level of exuberance that will, at very the very least, get supporters onside.
“You only need to examine their performance against Leeds to see the very best results. Solskjaer has opened up a clear pathway into the first team – and all parties concerned are reaping the rewards.”