The 26-year-old racked up a personal best of 294 runs in the series' third Test against India at Edgbaston.
Former England captain Vaughan is confident that this is just the beginning of an illustrious career for the Essex cricketer.
"I don't want to put him under too much pressure but he is going to get over 10,000 Test runs with over 35 Test match hundreds,” Vaughan is quoted as saying.
"He will probably be captain when Andrew Strauss relinquishes it in a few years' time and he has got a tremendous career ahead.
"He is the type of player you want, very determined, he grinds out every run. At times it is not pretty but, look at the end result, he is a run-scorer."
Meanwhile, pace bowler James Anderson remains a doubt for the fourth Test due to a thigh strain.