Babar Azam is currently ranked No.3 in the ICC Test batting rankings.
Root has been occupying the summit position since June as he dominated the home season against New Zealand and India.
The former England captain has scored more runs than any other player since the start of 2021 and deservedly earned the ICC Men's Test Player of the Year award.
"Tough one!" Jayawardena said on the latest episode of The ICC Review when asked who can displace Root from the top spot.
"I would say Babar Azam has an opportunity. He's been consistent in all three formats and it shows in his rankings. He's a naturally gifted player, plays in all conditions, he's got the game to adapt as well.
"It depends on the amount of cricket, who's playing when, and how much but the Babar might be the guy."
Babar is holding the top position in each of the white-ball formats and is currently ranked No.3 in the longest format.
"T20Is and ODIs, it is a tough one to hold on to because there are a lot of good players who have to be consistent," Jayawardena said.
"I would put my money on him at least for a little while to hold to all three but there are some good quality players around who will keep pushing him."
Mahela Jayawardena also explained what makes Babar Azam such a special player.
"(I) think it is just the technique, the time that he has, and the composure that he has out there in the middle," the former Sri Lanka captain said.
"He's not rattled at any time, whether he plays T20Is, ODIs, or Tests, he adjusts quite brilliantly.
"Joe (Root) in Test cricket is the same. He knows what he needs to do, he can the tempo when he wants to, bats to what the conditions offer. Babar has that same quality, so that's why he's been so consistent in all three formats."
(With ICC inputs)