Vaughan is regarded as one of the finest captains to have led England, masterminding the famous 2005 Ashes series win. He won 26 of his 51 Tests in charge between 2003 and 2008.
He added: “I look at someone like Ollie Pope, who looks a fantastic vice-captain. He is a brilliant person to have next to the captain to come up with ideas. Sometimes vice-captains aren’t brilliant captains.
“Marcus Trescothick was a magnificent vice-captain for me but you wouldn’t want to give him the captaincy.”
Pope, 27, is leading England in a Test for the fifth time. He previously stood in when Stokes had a hamstring injury last year.
Under Pope, the home side face an uphill task to win the decisive fifth Test. After being set 374 to beat India, a target that would represent their second-highest successful chase in a Test, they closed the third day on 50-1.
On Saturday, without the injured Chris Woakes, England were left relying on the trio of seamers Gus Atkinson, Josh Tongue and Jamie Overton.
Though they were eventually able to dismiss India for 396 in their second innings, England were hampered by six dropped catches.
“It is not Ollie Pope’s fault England are in this position. It is the dropped catches,” said Vaughan.
“There were a couple of times he nipped off the field. It might have been for a comfort break, but it looked like he was going off for tactical advice.
“I don’t know well enough and am not in the dressing room. I just want the best captain who is the best leader leading the England side. I don’t think a good vice-captain will necessarily be a good captain.”