Messi, 33, is out of contract at the end of the season and, since Jan. 1, has been free to negotiate a pre-contract agreement with other clubs.
Manchester City led the chase for Messi last summer when he told Barca he wanted to leave but PSG have been making the most noise in recent months.
Neymar said in December he hopes to play with his former Barca teammate again next season and PSG sporting director Leonardo confirmed the club are interested in Messi earlier this month.
Laporta -- who was Barca president between 2003 and 2010 and is the favourite to return to the role when elections are held on March 7 -- has warned that the lack of governance at the Catalan club is putting Messi's future in jeopardy.
"The club must be capable of making a good proposal that Messi is willing to accept," he said in a news conference on Wednesday. "That depends on the club.
"I would understand any answer [from Messi], but he needs to know what the proposal is; that requires urgency. It is getting more complicated all the time to make a convincing proposal. He's free to negotiate with other clubs now and Barca are still without a president.
"It is disrespectful to Barca that clubs like PSG publicly say they are going to sign Messi. This coming from a club-state that have bypassed the rules. We cannot allow clubs and states the luxury of destabilising another club.
"In that sense, we will have to speak with UEFA and FIFA to avoid such actions. PSG must abstain from [talking about Messi]. It is out of place for another club to speak about him. And, at the moment, there is no president in place to respond to this lack of respect."
Messi has stated he will wait until the end of the season before deciding where his future lies. He said in an interview in December that he will not take advantage of being able to speak with other clubs.
He returns from a two-game suspension on Wednesday as Barca face second division Rayo Vallecano in the last 16 of the Copa del Rey.
Despite all the noise surrounding his future off the pitch, he remains central to Ronald Koeman's side on it. In 22 appearances this season, he has scored 14 goals, including five in his last five appearances.