City, already the world's richest club after being taken over by Sheikh Mansour bin Zayed Al Nahyan of Abu Dhabi, face a potential banana skin in the fourth round of the FA Cup on Sunday when reputations often go out of the window.
Since Sheikh Mansour bought the club they have spent close to 200 million pounds on assembling a glittering squad.
City have suddenly become a threat after decades in the doldrums and living in the shadow of Manchester United but Cook's claim during a visit to New York was still a bold one.
"This football club is, without doubt, going to be the biggest and best football club in the world," he told a fans forum.
"I will make no excuses for saying it, as I truly believe it - with the resources and capabilities we have."
With a winnable FA Cup tie at Championship Scunthorpe on Sunday followed by the second leg of their League Cup semi-final with Manchester United on Wednesday when they will try and protect a 2-1 advantage, optimism is high at Eastlands.
They are also fifth in the Premier League and well-placed to challenge for a top four berth, even if the title looks beyond their reach this season.
While Cook speaks of global domination, manager Roberto Mancini's immediate priority is to make sure City do not become the fall guys in an FA Cup fourth-round shock.
"We must remember what happened between Liverpool and Reading, and United and Leeds as well," Mancini said of the two big third-round upsets.
"If we think about what happened in those two games, then we can go to Scunthorpe and make sure we win. It's a small ground, they will be strong because they are at home but we will have to be at our best."
