Manchester City striker Jesus scored his eighth international goal in last week's 3-1 win over Japan and appears set to play a key role at Russia 2018.
The 20-year-old Palmeiras product has already netted seven goals in his first full Premier League campaign, enough to convince Alves of his claims as the heir to the former Real Madrid legend.
And the Paris Saint-Germain full-back, who will captain his country on Wednesday, is adamant Jesus will not be affected by the comparison.
"I wasn't joking when I called him the new Ronaldo. They have a similar drive," Alves said.
"He's already great and will get even better.
"For all that he's done, all that he's achieved, there's no pressure. He's doing what he loves."