It is believed that PSG were contacted by Messi's representatives on Thursday after plans to stay at Barcelona stalled.
Intense negotiations have already taking place on Saturday as PSG is optimistic they can land the services of the 6-time Ballon d'Or winner this summer.
Barca disclosed that their former skipper is expected to address the press on Sunday at 11:00 BST.
The Catalan club on Thursday cited "financial and structural obstacles" as the reason to the exit of free agent Messi.
Barca president Joan Laporta, in a presser on Friday insisted that Barca would have been at risk for 50 years if they were to keep Messi at the club.
"I can't make a decision that will affect the club for 50 years," Laporta said.
"The club is over 100 years old and it's above everyone and everything, even above the best player of the world. We will always thank him for everything he's done for us.
"In order to have fair play, we need to do this or make an effort which would put the club at risk. We couldn't keep going with this and we needed to make a decision, which we have.
"Leo wanted to stay, so he's not happy," Laporta said.
"We all wanted him to stay. For him, he has to confront reality. It's a reality that can't be changed and he knows
I wish him the best wherever he goes.
"Leo's legacy is excellent. He's made history," Laporta said. "He's the player with the most success in history of the club.
"He's been the reference of an era which has been splendid. The best era of Barca's history until today.
"A new era starts now. There will be a before and after Leo. We need to be eternally thankful to him."
And with PSG aiming for a Champions League glory this season are said to be pushing for a deal for the 2021 Copa America winner.
Messi currently holds Barcelona's record scorer with 672 goals and has won 10 La Liga titles, four Champions Leagues, seven Copa del Rey trophies, including six Ballon d'Or glories.
