The Barca president said it would make "no sense" to pay money for players that both previously played for the club.
"Who doesn't like Ney?" Laporta told L'Esportiu when asked if he is a fan of the forward following reports he could come back to Barca.
"He is an exceptional player, but he has [three] years on his contract with PSG. He is effectively enslaved to money.
"The only way he could come back to Barca is for free. It would be irrational to pay a transfer fee for a player you have already had.
"Leo left how he left. We would all have liked him to end his sporting career here, but because of [LaLiga's] fair play rules and because of PSG's offer, it was not to be.
"If he wants to return one day, it would have to be for free. And the technical staff would have to decide if he fits the new project or not."
ESPN have reported that Mbappe would like a more balanced squad than what is there now given their lack of success in Europe, while the French club's owners have not been satisfied by his performances or his lifestyle.
Neymar has been at PSG since 2017, when the Ligue 1 champions paid a world record transfer fee of €222 million to activate his release clause and prise him away from Barcelona.
Messi, who will turn 35 in June, has one year to run on his contract in Paris after joining from Barca last summer.
Sources have told ESPN that any decision on his future beyond then will come after the World Cup, which he will compete in with Argentina later this year.
The Catalan club are also keen to sign a winger given the possibility of losing Ousmane Dembele, who is yet to sign a new contract with his terms up on June 30.
However, any transfer business will first be depending on Barca bringing in cash to make room within their LaLiga-imposed spending cap, with Laporta rallying against the Spanish league's regulations.
"We don't have any support from LaLiga," he added. "The fair play rules are too restrictive and demanding compared to other countries and it's a handicap.
"We respect the rules, but feel they are too strict compared to other countries. We are talking with LaLiga about this, but they don't seem to budge from their position.
"There are operations we are working on to improve the accounts, but LaLiga, instead of helping, try to harm us. It really surprises me."