Both Real and Barca are chasing the Frenchman, who also remains a target for Manchester United in 2018.
Zidane, reports Diario Gol, has been in touch with his countryman to remind him of how Barca treated the player eight years ago.
At the time, Barca only wanted to sign the attacker for their B team and with no guarantees of a first team promotion. Griezmann, who had played two full seasons with the La Real first team, found the offer insulting and immediately turned it down.
Zidane has been quick to remind Griezmann of the lack of trust Barca showed in his potential and is hoping this forces him to rethink any ambitions of moving to the Catalans.