The 26-year-old joined the Red Devils from Shakhtar Donetsk last summer in a deal worth around £52 million ($68m).
Although he started his side’s first three games of last season, the Brazil international was soon dropped by coach Jose Mourinho and was unable to cement a place in the starting XI.
Fred was given another chance under current boss Ole Gunnar Solskjaer, but was again left out for the final weeks and ended the season with just 17 Premier League appearances.
And while Rivaldo admitted that his compatriot’s maiden year in England has not been great, he challenged him to put up a bigger fight to secure a place in the first-team in 2019-20.
“Things haven't been easy for Fred at Manchester United and some people say he should find another club. But I disagree with that," he told Betfair.
“He is a good player who needs to be patient and keep working hard to earn a starting position in the United midfield.
“I don't think leaving would solve his problems, and it would be preferable to stay and keep fighting for his place.”
The 22-year-old is also yet to establish himself as a regular in the starting XI at his club, though he pitched in with 21 goals in 47 games in all competitions.
After seeing the striker play a crucial role in Brazil’s Copa America triumph – he scored and assisted a goal in both the semi-final and final, Rivaldo is sure he can impress Pep Guardiola and challenge Sergio Aguero for his place.
“Gabriel Jesus is full of confidence after a successful Copa America campaign for Brazil and looking forward to regaining his place in Manchester City's first team,” he added.
“He lost his place to Sergio Aguero last season, but I believe Jesus has the ability to be a starter in any team.
“The morale and confidence that he is bringing from Copa America could help him to become a regular starter and scorer for the Citizens this season.”