Ronaldo has found the back of the net six times in eight games since his return to Old Trafford and scored the winner against Atalanta in a 3-2 win for Manchester United on Wednesday night.
He is almost certain to occupy the number 9 position when Manchester United host Liverpool on Sunday in what is considered the biggest game in English football.
And Thompson stressed that as a Liverpool fan he is worried about Ronaldo and the impact he could have on the game.
He insisted that the Portuguese knows what is needed in big games and conceded that he has proved himself on the biggest of stages for club and country throughout his career.
The former Red feels Ronaldo is freakishly good for his age and believes if he continues to score goals for Manchester United his low running statistics will not matter to anyone.
Thompson said on LFC TV: “He knows all about them, he knows how big these [games] are.
“Yes, dare I say it, he worries me because this fellow turns up in big games. We have seen that for Real Madrid and Juventus.
“He has done it in different countries and he did for his own country.
“This guy is a freak of nature and I mean it so kindly. He is 36 years of age and you see him being a match-winner for them the other night with an unbelievable header.
“I have nothing but praise for this guy.
“Everybody is pinpointing his running stats, it’s probably the lowest of any striker in the Premier League, but it is what he produces in that box.
“If he scores goals and his running stats are down there and he keeps scoring goals in that box, everybody will forgive him.
“He will know, and he is one of those characters who will be saying we need to perform against Liverpool.”
Manchester United won five of the eight games they played against Liverpool with Ronaldo in their team during his first stint at the club.