Cook has been in horrible form during the home and away Ashes series this year, scoring 359 runs at an average of 25.64.
With his side 2-0 down in the current series, the pressure is building on Cook to perform in the third Ashes Test in Perth starting on Friday.
That match will mark Cook's 100-Test milestone and Prior said the 28-year-old, who boasts a Test average of 47.2, will be remembered as one of the game's all-time greats.
"I don't know the records Cooky's about to break, but there are going to be a few of them," Prior said on Wednesday.
"He will be one of - probably the greatest England cricketer.
"In my mind there is no doubt about that.
"And from a leader point of view, there's no other man that I'd want leading us out there, because one thing he does do is lead by the front and lead by example."
By rare coincidence Australian skipper Michael Clarke will also play his 100th Test in Perth this week.
Clarke has fared much better during the current series, plundering 284 runs at an average of 71.