Messi, 38, returned to Barcelona on Sunday to tour the revamped ground for the first time since leaving the club in 2021, later posting on Instagram that he hoped to "return one day, and not just to say goodbye as a player."
Laporta, speaking at a book presentation in Barcelona, said the board had already discussed plans for a permanent tribute to the Argentine World Cup winner.
"Messi will always be linked to Barca, he knows that the doors are open for him. We have absolute respect for him, he deserves the best tribute," he said.
"He should have a statue at Spotify Camp Nou, like (Johan) Cruyff and (Laszlo) Kubala. He is one of those iconic players who have left their mark on us. We have discussed it at a meeting and are working on it. The family must agree, and all Barca fans would want it."
Laporta previously dismissed suggestions that Messi could return to play for Barca, calling the idea "unrealistic" given the forward's contract with MLS side Inter Miami, which he extended last month.
Messi, who joined Barca's academy at 13, scored 672 goals in 778 appearances and led the team to 10 LaLiga titles, four Champions League crowns and three Club World Cups during his 21 years at the club.
The Camp Nou, closed for almost 900 days for renovation, reopened on Friday with an open training session attended by more than 20,000 fans. Laporta said the club hopes to host "the most beautiful tribute in the world" once the project is complete.