"There is no harm in dreaming of becoming the world's best player," he said
"Playing with the fantastic players we have here, I am in a very good position.
"It is all about trying to be the best. I will keep working hard to achieve it but it is within my capabilities."
He still wants to get one of the big prizes having won the FA and Carling cup during his time with the club.
"As a player, you try to improve everything about yourself," he said.
"I am very grateful to this football club. They have helped me a lot since I came here and hopefully I can become a big part of Manchester United history."
Ronaldo signed off his United season with the only goal in Roy Keane's testimonial at Old Trafford on Tuesday.
"I have a few tricks and dribbles which I use a lot and when I am playing well, it is natural they become easier," he said.
"But the tricks I use are ones that will hopefully benefit the team.
"I think I have improved a lot in the last few matches. I am getting used to the way defenders try and approach me and I think I am a more valuable team player now."