Greenwood, who will start against Astana when United begin their Europa League campaign on Thursday, has been a prolific scorer at youth level for club and country, scoring a goal a game in the Premier League Under-18 competition.
Although yet to open his account at senior level, the 17-year-old has impressed in his eight appearances, beginning with his surprise debut in the triumphant 3-1 Champions League victory at Paris Saint-Germain.
Solskjaer's praise is particularly noteworthy given his status as one of the most natural finishers in the Premier League during his time as a player at Old Trafford and the fact he played with other notable deadly finishers like Ruud van Nistelrooy and Cristiano Ronaldo.
"Mason is one of the best finishers I've seen," Solskjaer said. "And I've played with quite a few decent ones."
"When you've got strikers who can score goals, you should never lose the appetite...be ready to take your chances."
As for the advice he gives Greenwood, the Red Devils boss said: "Just work hard every single day. You've just got to keep working. The next game is always the most important one. It doesn't matter if you scored three last week. The next one is always the most important."