Griezmann has also been linked with a move after confirming he will leave Atletico Madrid this summer.
But Rivaldo believes the relationship Neymar has with Lionel Messi and Suarez means he would be a better fit for Barcelona over Griezmann.
“If I could choose one player to sign for Barcelona this summer it would be Neymar,” Rivaldo wrote for Betfair.
“The fans already know what he can do, he proved his value to the club last time he was there and he combines nicely with Messi and Suarez.
“He's also a good alternative to lead the attack when Messi isn't available.
Lionel Messi is why Barcelona should move for Neymar over Antoine Griezmann - Rivaldo (Image: GETTY)
Lionel Messi is why Barcelona should move for Neymar over Antoine Griezmann - Rivaldo (Image: GETTY)
“Griezmann is a great player but signing him would be more of a gamble, as he's never played at Barcelona or with Messi and Suárez.
“Of course, if he manages to perform like at Atleti he certainly could be a great addition to the team.
“But I prefer Neymar for the reasons I pointed out above. He knows the club and probably chats with Suarez and Messi regularly.
“Neymar's return might not make all the fans happy after the way he left for PSG, but if he helps them win the Champions League, fans would forgive anything.”
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