Solskjaer first met Greenwood at The Cliff - United's former training base - when he took his son Noah there for a training session in 2008.
Solskjaer, who was then United's reserve team boss, saw the teenage striker's talent straight away and asked the youngster's dad to have his picture taken with him.
“Mason, I actually do remember when I met him for the first time because my son was training at The Cliff as an eight-year-old," said the United boss.
“Mason was seven. The first time I saw him he stood out and I took a picture with him. I asked him because I knew he was going to be a player. He's probably got it or his dad has probably got it.
“His dad mentioned it to me and remembered him because I remember talking to Noah about it."