The Dutchman denied the Hammers a famous FA Cup victory over Sir Alex Ferguson's side by forcing a replay with a 90th-minute equaliser at Upton Park on Saturday.
And Cole, who grabbed two assists during that game as he marked his first appearance since returning to his boyhood club from Liverpool, has hailed Van Persie's quality.
"You take away [Lionel] Messi and [Cristiano] Ronaldo and Van Persie is probably the best player in the world,” he told the Guardian.
"He was playing wide for Arsenal for many years and getting a few injury problems but moving central means there is a bit less running and he can use his technique and finishing, which is just incredible.
"He is a joy to watch and a pain to play against."
Van Persie has scored 20 goals in 26 appearances since his summer move to Old Trafford from Arsenal.