Vice president Rafa Yuste confirmed Friday that the club are looking into the possibility of re-signing Messi, who left for PSG in 2021, with coach Xavi Hernandez later adding he hopes to see the Argentine back at Spotify Camp Nou.
"I am still gutted he couldn't continue here," Yuste said at a news conference. "Of course I would like him to come back, because of what he represents on a sporting, social and economic level.
"We are in contact with [Messi's camp], yes. Beautiful stories should have happy endings, and there is a mutual love between the two parties."
Messi, 35, left two years ago after two decades in Catalonia because Barca could not afford to renew his contract. The financial side of any return this summer remains an obstacle.
Barca need to knock more than €150 million off their annual spending -- or raise money through transfers -- to comply with LaLiga's economic regulations and be able to sign players and register contract renewals.
"We still have two months to work hard to present our revenue and sustainability plan to [LaLiga president Javier] Tebas," Yuste added when asked whether bringing Messi back was really possible.
"I don't like to speak about Leo because he is a PSG player, but if all the conditions are met, we are open to the possibility. [Barca] president [Joan Laporta] has been with Leo's father, and there is a good relationship.
"Of course, there is no plan to go on the attack because we don't want PSG to see it like that. If it happens, it will be because destiny takes you back to where you have to go. If all the conditions come together and Leo comes back to Barcelona, it would be the perfect ending to a very happy story."
Barca coach Xavi, who played alongside Messi, said it depends more on what the Argentina forward wants to do next than money, with a renewal at PSG and a move to Major League Soccer other possibilities.
"There is the fair play issue, but more than anything it depends on Leo's intentions and [if he wants] to come back," he said in a news conference ahead of Saturday's trip to Elche.
"A lot of conditions have to fall into place for it to happen. He's won everything in the game, and it will depend on his happiness. If he wants to come back, if that's his intention, we will speak about it.
"We are friends, we speak often, but it's not the moment to talk about this, for the good of Leo, the club or the squad. It's an issue we're dealing [with], but from that to [him returning] is a big leap.
"I hope we see him come home. I'm the first person who would love to see the best player ever return. And it is normal that fans are excited about a 'Last Dance' like [happened with] Michael Jordan."
PSG coach Christophe Galtier said on Friday he is trying to focus only on the season at hand rather than address questions about Messi's future.
"I know that Messi and the club [PSG] have been in negotiations for a while, but what Leo decides to do with his future is confidential and that is not for me to discuss," Galtier said. "I am not the person to make the decision and the club will decide about Messi's future."
Elsewhere, Xavi played down the importance of comments made by Ansu Fati's father, Bori, this week, suggesting the player should look for a new club in search of more minutes.
Xavi said that he understood Bori's frustration but that he was concerned only about Ansu, who, he added, is "focused, training well and relaxed."
"I suppose the problem is he's a Barca player; if he was playing for another team, I guess [his attitude] would be a virtue," he said.
"He is one of the best midfielders in the world right now, no doubt. If he played in another team, he would be treated differently.
"I don't understand how there can be a campaign against a kid aged 18 who has come through like he has and plays like he does. It surprises me. It doesn't matter where he plays, he should be admired. I supposed it is down to the rivalry."
Barca return to LaLiga action against Elche this weekend with a 12-point lead at the top of the table, although they are missing Frenkie de Jong, Pedri, Ousmane Dembele and Andreas Christensen through injury and Raphinha through suspension.