Brook slammed a triple hundred in England's historic win over Pakistan in Multan Test.
Brook starred with the bat in England’s innings and 47-run victory over Pakistan in the recently held Multan Test. He slammed an explosive triple hundred (317 off 322) in the match.
In the same Test, Root scored a double century (262), which took his runs tally to 12,664 runs. The 33-year-old now occupies the fifth spot on the all-time list.
"He's on the way to being in the top three that I've played with," Anderson said on the Tailenders podcast. "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, who announced his retirement from international cricket in July this year, finished his Test career as the third-highest wicket-taker with 704 wickets from 188 matches.
Having played alongside both Pietersen and Root, Anderson feels that Brook possesses the latter's technique and temperament.
"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."