Anderson needs eight wickets to move past Ian Botham's English test record of 383 and whether or not he achieves that at the Oval starting on Friday, Cook is in no doubt that the 32-year-old belongs alongside the very best.
"It's an amazing achievement," Cook told a news conference on Thursday in which he confirmed that Anderson's opening partner Stuart Broad would be fit for the series decider despite sustaining a broken nose in the last test.
"If he does it in this game it will mean England are in a very strong position.
"No disrespect to Dale Steyn in terms of actual skill, but the way that Jimmy can swing the ball both ways I don't think Dale does that quite as well as Jimmy, although Dale has the advantage of being able to bowl quicker.
"You would put both of them in the same class."
England have emerged from a dismal sequence of 10 test matches without a win to come from 1-0 down against India to lead 2-1 after emphatic victories in Southampton and Manchester.
Cook has also returned to form with the bat but said England would not be relaxing - or looking for a draw to clinch the series victory.
"There has been a massive turnaround, so the guys can take a lot of credit for the way they have turned it around and if we are sitting here at the end with a trophy it would be brilliant," he said.
"We are not going in with any other mindset other than it's a game to win," Cook added.
"We are not thinking if we survive this we will win the series, we need to have the mindset we had after Lord's when we came out fighting.
"Just because we won a couple of games we won't relax at all. The atmosphere has lifted a bit but we have to earn the right to put in a good performance."
England thrashed India by an innings and 54 runs inside three days in the fourth test at Old Trafford on Saturday.
Broad took six wickets in the first innings and was unable to bowl in the second due to his injury. Anderson had five victims in the match.
(Reporting by Martyn Herman, editing by Ed Osmond)
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