Red Devils' young superstar scored in his fourth consecutive Premier League match in Saturday's victory over Brighton and left his new boss talking about the three Rs.
Rashford's strike saw him break Cristiano Ronaldo's record as the youngest United player to score in four successive league games on what was his 150th outing for the club.
And Solskjaer put the 21-year-old on a par with Ronaldo and Wayne Rooney.
United chief said: "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."
Until Saturday, Ronaldo had held the record as the youngest United player to score in four straight league games.
Now a veteran at Juventus, the Portuguese superstar made that mark on December 8, 2007 at the age of 22 years and 306 days.
Rashford beat that comfortably with the new record standing at 21 years and 80 days.
Asked whether Rashford belonged in the same bracket as Ronnie and Roo, Solskjaer didn't hesitate: "Definitely. He can be absolutely top-class.
"He's playing the best football of his career. He's got a great future."
But it's the present Solskjaer will be focusing on as the Old Trafford favourite looks to land the manager's job on a permanent basis.
Rashford has been key to Solskjaer's early success and the former striker's influence is clearly rubbing off on the young buck.
He will hope the run continues when United travel to the Emirates Stadium on Friday for the highly-anticipated FA Cup fourth round clash with Arsenal.
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