Messi, 30, agreed a four-year deal with Barcelona in July, although has not officially signed it yet.
Grau, speaking at the club's annual general meeting, said the Argentine forward would be offered a similar deal to the one Barca's Spanish midfielder Andres Iniesta signed this month.
"Messi signed a four-year deal in June, but the club will offer him a lifetime contract," Grau told club members.
"The idea is for Leo, who has been here since he was little, to stay here for life, as he is an icon. After he finishes playing we want him to remain linked to the club."
(Reporting by Rik Sharma, editing by Ed Osmond)
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