Solskjaer’s coming off his biggest win as manager, having led his side to a famous 3-1 victory against Paris Saint-Germain at the Parc De Pricnes on Wednesday.
Manchester United overturned a 2-0 deficit from the first leg at Old Trafford to win the tie on away goals.
Rashford started both games for United and in the away leg he was pivotal in Romelu Lukaku’s second goal of the game, providing a palm-stinging shot that veteran goalkeeper Gianluigi Buffon couldn’t hold on to.
The 21-year-old then stepped up to take a vital 94th-minute penalty in Paris that saw his club advance to the quarter finals of Europe’s elite competition.
Marcus Rashford has enjoyed his best ever goal=-scoring season so far, having notched nine in the Premier League and six in his last 11 games.
But Solskjaer, whose career at Old Trafford spanned 11 years under the tutelage of Sir Alex Ferguson, insists that Rashford becomes more clinical inside the box.
“I keep battering him with that he also should score as many goals as Rom [Lukaku],” Solskjaer said.
“You should always get those simple tap ins, finishes, like Rom’s scored the last few games.
“Rashy’s goals sometimes are worldies and he does have a sensational strike of the ball.
“But you see the change in Cristiano Ronaldo’s goals from when he was young to now, he scores more from inside the box and that’s what Rashy has to improve as well.”
Solskjaer then went on to note that his hopes for Rashford include becoming a one-club legend like Ryan Giggs, Paul Scholes and Gary Neville.
Rashford made his debut for the club in 2016 against Midtjylland in the Europa League, scoring two goals.
“We all know all the legends we’ve had at this club that have stayed so long and they’ve been one-club players and we hope that Rashy is going to be one of them,” Solskjaer added.
“It’s both up to him and us of course.
“If he keeps producing he’ll stay in the team and that’s up to him to stay in the team.”