Valverde is less than impressed with Luis Suarez this season and is ready to give him the bullet.
Suarez is playing through pain this season and needs to undergo surgery.
But with Ousmane Dembele out he has decided to play – but without much success.
The 30-year-old has still managed six goals in 11 games but some of his displays have drawn criticism, and Valverde wants an upgrade.
And the man he wants, according to Don Balon, is Atletico Madrid star Griezmann.
But Messi is desperate for Valverde to stick with Suarez and believes his place in the team should be guaranteed.
Messi has struck up a close relationship with the former Liverpool man and doesn’t want someone to rival his place.
Barcelona spent nearly £100m on Ousmane Dembele last summer and if another man came through the door it would mark a new era up top.
Messi, Dembele and Griezmann would be Valverde’s first choice trio leaving Suarez on the sidelines.
Barca are top of La Liga after 14 games and have left Real Madrid in their wake.
Valencia are the nearest challengers and are already five points behind, with Madrid a further three and down in fourth.
Griezmann has had an indifferent season at Atletico this term and is likely to quit in the summer after rejecting a move this year.
Manchester United are expected to make another move so Barcelona would need to make their approach early.