Rashford reached the landmark on Saturday and scored to help the Red Devils earn a 2-1 win over Brighton and Hove Albion.
Per the Daily Mail's Chris Wheeler, Solskjaer said of the 21-year-old:
"If you look at the stats, I was told that he is younger than Ronaldo and Rooney to reach 150 appearances for Manchester United.
"Not bad, is it? The 150th game is a feat in itself, being 21, but with the level of his performance, the maturity in his finishing and his work rate, it's a dream to have players like him in the team."
When asked if Rashford can be compared to Rooney and Ronaldo, Solskjaer replied: "Definitely. He can be absolutely top class. He's playing the best football of his career. He's got a great future."
The striker scored a fine goal against the Seagulls. After picking the ball up from Diogo Dalot to the left of goal, he turned Pascal Gross before curling the ball into the top corner.
Football analyst Dave O'Brien shared his impressive career numbers:
It was his fifth goal in six Premier League matches since Solskjaer took charge and ninth of the campaign overall.
Match of the Day host Gary Lineker and Samuel Luckhurst of the Manchester Evening News noted the impact Solskjaer has had on Rashford since his arrival in December:
The former striker discussed the work he's done with Rashford during his time at the club:
"You're on the training pitch with him, but it's more talking to him and getting inside his head. That's what I like the most, to find out what he's thinking.
"He'd missed a couple of chances before I arrived and the first thing I said to him when I met him was, 'No, problem, you'll be all right as long as you settle down a little bit.'"
His words seem to have had a profound effect on the youngster's form thus far, and his comparison to Rooney and Ronaldo isn't too outlandish.
Per Squawka's Chris Smith, Rooney scored 45 goals in his first 150 club career appearances, while Ronaldo netted 25 times. Unlike Rashford, whose entire career has been with United, their first 150 games included their beginnings at Everton and Sporting Lisbon, respectively.
Rashford has a long way to go before he can compare with what Rooney and Ronaldo have gone on to achieve in their storied careers, but it has been a promising and exciting start from him.