Messi suffered a knock on his left knee and an MRI scan earlier this week confirmed signs of a bone contusion. He missed PSG’s 2-1 victory at Metz on Wednesday.
The Argentina forward, who joined the French club from Barcelona on a two-year contract in August, will be assessed again on Sunday — ahead of next week’s Champions League home game against Manchester City.
Speaking at a news conference on Friday, PSG coach Mauricio Pochettino said: “Leo has started running today. On Sunday we will be able to give an update. We hope everything will go well and that he will be available again [for the game vs. Man City].”
PSG added midfielder Marco Verratti will return to training on Sunday while defender Sergio Ramos, who has yet to make his club debut, continues to train individually as he recovers from a calf injury.
The club are top of the Ligue 1 standings with a perfect win record from seven games.