Messi's 21-year stay at Barca came to an end in the summer as the club were unable to tie him down to a new contract amid a financial crisis that had seen them exceed La Liga's wage limit, goal.com reported.
The 34-year-old subsequently joined PSG on a free transfer, but Laporta has since suggested that the legendary figure could have stayed at Camp Nou if he had been willing to go without a weekly salary.
When quizzed on Messi's move to Parc des Princes, the Barca president told RAC1 in October: "I hoped Messi would do a U-turn and he would say he would play for free.
"I would have liked that and I would have been all for it. It is my understanding La Liga would have accepted it. But we cannot ask a player of Messi's stature to do this."
Messi has now hit back at Laporta for raising doubts about his strength of character instead of taking responsibility for his exit, while also reiterating that he did everything possible to remain at Barca.
"The truth is that, as I explained on my way out, I did everything possible to stay, never at any time was I asked to play for free," the Argentine forward has told Sport.
"I was asked to cut my salary by 50 per cent and I did it without any problem. We were in a position to help the club more. The desire of me and my family was to stay in Barcelona.
"Nobody asked me to play for free but at the same time, it seems to me that the words said by the president are out of place. They hurt me because I think he doesn't need to say that, it's like getting the ball off you and not assuming its consequences, or taking charge of things.
"This makes people think or generates a type of doubt that I think I do not deserve."
Messi also discussed his chances of winning the Ballon d'Or for the seventh time in December, having helped Barca lift the Copa del Rey in his final season at the club before securing his first piece of international silverware with Argentina at the Copa America.
Pressed on whether he expects to land a second successive Ballon d'Or, Messi replied: "If I'm honest, I don't think so. My biggest prize was what I was able to achieve with the national team. After having fought and fought so much for that achievement, it was the best for all it cost.
"If the Ballon d'Or arrives it would be extraordinary for what it would mean winning one more. The seventh would be crazy. If not, nothing happens. I have already achieved one of my great goals."
It has been suggested that Messi could retire from international football after the 2022 World Cup in Qatar, but he claims that the thought has not yet crossed his mind.
"No, not really. Not really. After what happened to me, I live day by day, year by year," the ex-Barcelona captain added. "I don't know what will happen in the World Cup or after the World Cup. I don't think about it. Whatever has to happen at that moment will happen."
Messi also said he will return to live in Barcelona with his family when his time at PSG is over and would like to help the La Liga club in the role of a technical director.
"I always said that I would love to be able to help the club ... I would love to be a technical director at some point. I don't know if it will be at Barcelona or not.
"If there is a possibility, I would like to contribute again because it's the club that I love and I would love for it to continue doing well, to continue growing and to continue being one of the best in the world."