The Portugal international, 23, has surprised himself with his performances as United retained the Premier League, but he is determined to cement his status with victory over Chelsea in Moscow on Wednesday night.
"I have been totally surprised by how many goals I have scored as I am not even a centre forward," he told the Daily Mail.
"But to be the best in the world I have to win titles like the Champions League and the Premier League.
"I am a winner and I have a dream that we will win the double this season. It would be madness if we did but why is it not possible now?
"It is not easy to win anything, especially not the Champions League. I think if you win that then you go down in history and that is what I want."
Ronaldo revealed he is feeling fresh ahead of the Champions League final and the European Championship.
He said: "No player gets tired when they are winning games and trophies. This is the type of situation now that players dream of. Manchester United is a 'superclub' and we are obliged to win things every season. So tiredness does not come in to it.
"Next season we will be obliged to repeat what we have done and I'm sure that we will."