Rashford scored in United's 2-1 win over champions Manchester City at the weekend to take his tally to 10 league goals for the season, already equalling his best return in the top flight midway through the campaign.
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The 22-year-old England international has 13 goals in his last 14 games for club and country and Solskjaer said he saw similarities with Portuguese forward Ronaldo, who scored 118 times in 292 appearances for United from 2003-2009.
"It's very easy to compare the two of them, yes," Solskjaer said.
"Both with skills, body shape, attitude, attributes - everything. The boy has every chance in the world to become a top, top player. Let's hope he continues like this."
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Rashford has previously been criticised for a perceived lack of composure in front of goal but he is flourishing under Solskjaer, who scored 126 goals in 366 appearances as a player for United.
The Norwegian said there was much more to come from Rashford.
"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," Solskjaer said.
United, who are fifth in the Premier League, face Dutch side AZ Alkmaar in the Europa League on Thursday.
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