Rashford has scored 13 goals in his past 14 games for club and country including a penalty in United's 2-1 win over champions Manchester City at the Etihad Stadium on Saturday.
Solskjaer was a player at Old Trafford as Ronaldo transformed from promising youngster into one of the best players in the world and the Norwegian said he believes Rashford is on the same upward trajectory.
"It's very easy to compare the two of them," Solskjaer said. "Both with skills, body shape, attitude, attributes -- everything.
"The boy has every chance in the world to become a top, top player. Lets hope he continues like this."
Rashford's derby goal moved him on to 10 in the Premier League and 13 in all competitions, matching his season's best tally with six months of the campaign still to play.
The 22-year-old has had most of his success as a left winger and Solskjaer said he is offering more to the team than just putting the ball in the net.
"I don't want to talk about the amount of goals," Solskjaer said. "As long as he keeps being positive and being direct and thinking about getting in front of the goal and getting chances, he'll score goals."