Despite having lost yesterday's clash with India at Edgbaston by nine wickets, which sealed a series victory for the tourists in the process, Cook remained defiant regarding his position in the face of criticism from the likes of Sir Ian Botham and Graeme Swann.
However, with the World Cup coming up early next year, Vaughan believes that if Cook does not stand down from the role, he should be sacked for the good of the team.
"With six months to go, other teams are looking at this side and hoping that Cook remains as captain, and opens the batting at next year's World Cup, because they know if that happens England will not be a threat," the former England skipper wrote in The Telegraph.
"The rest of the world see one-day cricket through Twenty20 eyes, whereas England see it through Test match eyes. I think it is getting to the stage now when that harsh reality has hit home for England. Cook is a stubborn man. He proved it this summer when he defied people calling for him to go and made his point by winning the Test series against India.
"One-day cricket is different. If he is not going to stand down then the tough call has to be made. If he is not willing to resign and [national selector] James Whitaker and Paul Downton, the managing director of England cricket, can't see that a change needs to be made, then I seriously question the vision of the men making decisions in English cricket."
England get their World Cup campaign underway in Melbourne on February 14.