Suarez has endured a difficult season for Barcelona so far, with the Uruguay international a far cry from the player that helped fire the club to the La Liga title two years ago.
As a result of his plight, talk has been rife that Barcelona could be set to replace him with Atletico Madrid hitman Antoine Griezmann.
Griezmann nearly left Spain for Manchester United back in the summer, only to end up staying put in the wake of Atletico’s transfer ban.
And Don Balon say that Messi is not keen for Griezmann to make the move to the Nou Camp as Suarez’s Barcelona replacement.
Former Liverpool striker Suarez has just three goals from 14 outings so far this season.
And Barcelona put Sevilla to the sword on Saturday with reserve forward Paco Alcacer bagging a brace.
Griezmann’s own troubles at Atletico are well-documented with the France international scoring just three goals as well.
And Don Balon claim that Messi does not want the striker signing if it means Suarez being shown the door.
He supposedly thinks Barcelona should do everything to keep him for the long term.
It was also reportedly why goalkeeper Pinto was at the club for so long – merely because he always had the backing of Messi.
Meanwhile, Barcelona boss Ernesto Valverde thinks Suarez remains a key asset – despite him failing to hit the goal trail.
“We talk a lot about Suarez lately, but I’m pleased to have him because of how he works and all the things he gives us,” he said.
“He is a killer.
“Despite the fact he’s not scoring lately, he always has chances, [against Sevilla] too. And that is a good sign.”