He also came third in the FIFA Ballon d'Or awards behind team mate Messi and Real Madrid's Cristiano Ronaldo in January.
"If we speak about the best, it is Leo Messi. Neymar is on the way to be the next best," Rakitic told the Times.
"Barca will do the best thing to sign a new contract with him and maybe they can put a buyout clause as high as possible, because he will be the next Messi for sure."
"He's scored (nearly) 300 goals and he's only 24. He's really special."
Croatia international Rakitic, who joined Barca in June 2014, believes striker Luis Suarez's spell at Liverpool made him the most feared striker in the world.
Suarez was top scorer in the Premier League and claimed the Professional Footballers' Association and Football Writers' Player of the Year awards at Liverpool in the 2013-14 season, inspiring the club to second-place top flight finish.
"The years at Liverpool were really important for Luis. There he takes the change from a good player to be the best striker in the world and then do the next step at Barcelona, Rakitic added.
"When he's not playing; it feels something's wrong. Luis is one of the most important players for us. He's a really good guy in the dressing room, one of the most open people who likes to joke."
(Reporting by Ian Rodricks in Bengaluru; editing by Amlan Chakraborty)
