Cook is determined to take all the time available to him so he makes the right decision about whether to continue in the role.
After England had suffered a second successive innings defeat on Tuesday to finish 4-0 series losers in India, Cook said he was in no state to make the call on whether he extends his four-year reign at the helm.
England do not play Test cricket again for more than six months, with South Africa their next opponents in July, but former England captain and Yorkshire star Vaughan believes Cook is ready to walk away.
“His body language over the last three matches was one where he looks like he might be thinking of calling it a day,” said Vaughan.
“He’s earned that right to have a period of time at home. We’ll wait and see.
“He’s stubborn and mentally very tough. He’s been through this sort of spell two or three times in his captaincy and carried on.
“But he has to be very honest with himself. Does he have the passion and energy to take the team forward through the seven Tests next summer? And then through the Ashes next winter?
“I would think it’s very close to being the time to call it quits from his perspective.”
Cook - who will be 32 on Christmas Day - has been in charge of 57 Tests since he became permanent England captain in August 2012.
He plans to meet England and Wales Cricket Board director Andrew Strauss next month about the future direction of English cricket.
“They’ll meet up, they’ll have a good chat. It just needs some honesty,” Vaughan said.
“Andrew Strauss has got to say to him ‘Cookie, have you got the energy?’ You need to have so much energy to lead your country.
“I am seeing in Alastair Cook a player who is not enjoying the game.
“This England team are a great set of lads and Alastair Cook is the nicest lad in the world but he has had a stinker (in India). Some of his tactics have been all over the place.
“It is more important to get Alastair Cook’s runs in Australia and, if it means him not being the leader to get those runs, I’ll take that.”