The Argentina international is locked in negotiations with the La Liga giants about an extension to his current contract, which is due to expire in 2018, with wages thought to be the sticking point.
Responding to the comments, however, Suarez pleaded with Grau to put aside his stance and do whatever it takes to tie down the hitman for the long term.
"Messi is the best player in the world," he told Marca. "What has to be done is that the club needs to renew his contract and to not use common sense."
Suarez penned fresh terms last month keeping him at the side until 2022.