He has not yet renewed his deal with the Ligue 1 champions.
"It will be his last game this season," the source told Reuters.
Messi, who led Argentina to the World Cup title in Qatar and also boasts a record seven Ballon d'Or awards, won the Ligue 1 title in the 2021/22 and 2022/23 seasons with PSG as well as the French Super Cup in July 2022.
"I had the privilege of coaching the best player in the history of football. This will be his last match at the Parc des Princes, and I hope that he will receive the warmest of welcomes," Galtier told reporters on Thursday.
Last month, French media reported that Messi was suspended for two weeks after an unauthorised trip to Saudi Arabia when he was supposed to train with his team following their 3-1 defeat at home to Lorient in the league.
"This year, he has been an important part of the team, always available. I don't think any of the comments or criticisms are justified," Galtier said.
"He's always been there for the team. It's been a great privilege to accompany him throughout the season."
Messi's future at PSG had been the subject of much speculation recently, with a source close to the Argentina captain telling Reuters that he had received a formal offer to join Saudi Arabian club Al-Hilal next season.
He has also been linked in the media with a move back to boyhood club Barcelona, with the United States' Major League Soccer club Inter Miami also being touted as a possible destination.
PSG's title celebrations on hold
Rico was involved in a riding accident while participating in an annual pilgrimage in southern Spain, the day after PSG wrapped up the title with one game to spare.
Rico has been in intensive care after suffering "a serious mishap due to a mule cart and a horse that hit him", his family said in a statement late on Sunday. Spanish paper Marca reported that Rico had been riding a horse himself.
"There will be no celebrations, it's been a very difficult week. We're all affected because we went from winning the French title on Saturday to waking up in more than a little pain on Sunday morning," Galtier told reporters ahead of PSG's final league game of the season.
"We're all affected, and we're trying as best we can to take our minds off things through the training sessions... We're very united in sending out lots of positive vibes and energy to Sergio, his mum, his wife and his loved ones."