Brook became the first England batter in 34 years to score a triple-century when his side thrashed Pakistan by an innings and 47 runs on the fifth day of their opening Test of the three-match series in Multan on Friday.
Root made a double ton during the same test, placing him fifth on the all-time list with 12,664 runs.
"He's on the way to being in the top three that I've played with," Anderson said on the Tailenders podcast on Friday.
"It's Root, Pietersen and him. He's definitely got all the attributes to overtake them.
"He's just got everything. Without trying to big him up too much because he's still really early in his test career, I do think that he's got the perfect amount of each of those two and that's what will make him the best that we've ever had."
Anderson retired in July after finishing his 188th test and having taken 704 wickets in a career spanning 21 years, during which he became the third-highest wicket-taker in the format.
Having played with Root and Pietersen, Anderson believes Brook has the temperament and technique of the former.
"But he's got the shots of both Root and Pietersen. He can destroy an attack if he wants to, he can play a longer innings if he needs to," Anderson added.
"The thing that's really similar between Root and Brook is that they love batting. They literally couldn't care less what format it is. They just want to bat.
"They want to have fun doing it. As much as Brook's the younger player and will be learning loads from Rooty, I still think Rooty learns from him as well."