Gallardo has been linked with Ernesto Valverde's job.
And Rivaldo told Betfair: "Of course I believe he could coach Barcelona. He's preparing for that. His work at River Plate has been fantastic. He won the Libertadores last year. He's at the point where he's ready to go to Europe and manage a top side like Barcelona.
River Plate take on Flamengo in Lima, Peru and another victory could establish the Argentine side as one of the greatest ever teams. "If River win back-to-back Libertadores, everyone on the planet will be talking about them."