The Argentina international, a part of the Barca fold since 2001, has still yet to formally put pen to paper on the four-year deal offered to him during the summer.
Negotiations continue to rumble on between player and club, but Grau is hopeful of seeing Messi agree a similar contract to the one signed by teammate Andres Iniesta earlier this month.
"The idea is for Leo, who has been here since he was little, to stay here for life because he's an icon," he told reporters. "After his playing days we want him to continue to be linked to the club."
Iniesta 'signed a lifetime contract' at Barcelona on October 6, having also seen his future constantly called into question.