Greenwood, who bailed out the Red Devils in their Europa League tie against Astana bulged the net again in a 1-1 draw fixture with Rochdale before winning 5-3 on penalties at the Old Trafford on Wednesday.
Despite Greenwood's incredible performances for Manchester United, Solskjaer preaches for patience for the 17-year-old to help him grow well with his talent.
“We always want some quality in the last third and we lacked that at times," Solskjaer said.
"They defended well but we should have scored quite a few goals. We should have taken our chances, but we've got Mason.
"It's a good finish, he's right-footed, left-footed, takes the penalty with his right and scores with his left, so he's a confident finisher.
“You’ve got to remember he's 18 next week so give him time, he'll be a very good player.
“We’re through so we're happy with that," he added.
“That’s the first plus, then the fans are a plus, and then the penalties, the players enjoyed taking them."
Booking a place in the round 4 of the Carabao Cup after downing Rochdale, Solskjaer’s Man United will host Unai Emery’s Arsenal in a blockbuster showdown in the Premier League on Monday.
Starring in the last two games for the club, Greenwood could be named in the match-day squad due to the absence of Marcus Rashford and Anthony Martial as they all join United's injury woes.
After six games thus far, United are eighth in the table with 8 points, recording two wins, two losses and two draws.
