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 Tuesday, 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 at Brazil's pre-match press conference.
"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."
Alves' comments received support from Brazil boss Tite, who is hoping to build the Selecao around its young star.
"Any player of Jesus' level really needs a team behind him," the manager said.
"An athlete of that level can only shine with the team and that's what we're hoping for here.
"Manchester City should be very happy with Palmeiras, who formed an athlete who was already prepared. He had a natural fluency when he arrived [in England]."
Brazil are expected to field a full-strength team against Gareth Southgate's side, with Philippe Coutinho tipped start despite sitting out Liverpool's last three matches.