Messi, who has been a free agent since his contract expired at Camp Nou on June 30, had maintained his silence since Barca announced on Thursday that he will not sign new terms because of financial problems.
The Argentina forward said he had received several calls from clubs since the news broke, confirming PSG's interest, and multiple sources have told ESPN that he has already agreed to sign for the Ligue 1 side.
Sources added that Messi is expected to travel to Paris soon before completing a medical in the coming days and signing a two-year deal with the option for a third season. He could be presented at an event at the Eiffel Tower in the coming days.
"[PSG] is one possibility," Messi said. "There's nothing closed at the moment, but we're talking about a lot of things. After Barca's statement, a lot of clubs showed an interest. There's nothing final but, of course, there are talks."
Asked about the prospect of joining a rival, he added: "There is no doubt that I will go to a team that will compete with Barca. I didn't want to leave, but I have to. And I want to keep winning. That's my mentality. I want to win."
Messi said a photograph of him with several PSG players in the Spanish island resort of Ibiza last week, including Neymar and Angel Di Maria, was just a coincidence, although he said they did joke about him moving to Paris.
Instead, in an event at the auditorium to the side of Camp Nou attended by the board, the first-team squad and his family, Messi insisted he had done everything possible to stay at Barca.
"I am really sad because I didn't want to leave because this is the club I love," he said. "I didn't expect this. I have never lied; I have always been honest and upfront. Last year I wanted to leave; this year I didn't. That's why I am so sad.
"As the president [Joan Laporta] has explained, the club has debt [problems]. It's not possible. Why keep drawing it out if it's nearly impossible? The talks stopped as Barca did not want to go on, they knew LaLiga would not let it happen, it was impossible.
"I did everything I could to stay and it wasn't possible. I offered to reduce my salary by 50% and Barca didn't ask for anything else. They didn't ask for another 30%; that's a lie."
Messi, 34, had agreed to a new five-year contract with Barca, but that would have meant the club's wage bill stood at 110% of their revenue. Their spending cap with LaLiga has dropped from over €600 million in 2019-20 to an expected €200m for the coming season, making it impossible to register Messi's new deal, even with a big pay cut. His previous terms included a base salary of around €70m gross without bonuses.
He wrote a farewell message on social media which read: "I would have liked to leave in another way, although I suppose that a farewell can never be something nice. I would have loved to continue here, I did everything with that objective and in the end it did not happen.
"I only have words of thanks for all those who have accompanied me in so many years at the club. And for our fans, that they gave me all their love and that I tried to give it back to them, also giving everything for this shirt. I'm leaving but it's not goodbye, just see you later. Visca el Barça!"
Messi also lamented that he had been unable to say goodbye on the pitch with the fans chanting his name, bemoaning that his last 18 months at the club have been played in empty stadiums due to the pandemic.
"Without a doubt, this is the most difficult time of my career," Messi added at the news conference. "I have had a lot of tough moments, but the other day, [learning I was] not going back to training, not going to be on the pitch again, that this is the end with this club, yes, it's one of the most difficult moments for me.
"This year is different from last year [when I wanted to leave]. My family and I were convinced we were going to stay, that's what we wanted more than anything. We are at home here. Now I have to say goodbye to all of this. I have been here since I was 13. After 21 years, I am leaving with my wife, with my three little Catalan-Argentine kids. I can't say that we won't come back in some way because this is our home and I promised my children we would."
LaLiga also posted a tribute on social media and said: "We made history together. It's been a matter of pride to see you become a legend. Thanks, Leo Messi."
With 672 goals in 778 games for Barca, Messi leaves as both the club's record appearance maker and top goal scorer. However, he says no one person comes before the club and assured supporters there is a squad built for success even without him.
"Barca are one of the best teams in the world, they have an amazing side," he said. "More players will come, not just now but in the future. Players come and go. As Laporta said, no one person comes before the club. At first, it will be weird, but people will get used to it."
Messi's wife, Antonela Roccuzzo, also posted, writing: "How difficult it is to summarise in a few lines all these past years! "So many emotions that left their mark forever in our lives ❤️ "But as the saying goes, what does not kill us, strengthens us! And with the family as a base, we will go out to the pitch again, stronger than ever ... ❤️Let's go wherever we go together, but always forward !!!!! ❤️❤️ "I love you my love!!! ❤️ @leomessi."