Van Persie stole the FA Cup limelight by scoring his 20th goal in a United shirt to earn his team a replay at Old Trafford on January 16.
"You take away Messi and Ronaldo and he's probably the best player in the world," said Cole. "He is different class and in his prime. He is hard to stop and he is just sublime. Technically, he is fantastic.
"He was playing wide for Arsenal for many years and getting a few injury problems. Moving central means there is a bit less running in there and he can use his technique and use his finishing, which is just incredible.
"He uses both feet. He is a joy to watch and a pain to play against. It was just a world-class ball from Giggs and a world-class finish."