Messi signed an optional third-season clause in his contract when he first arrived in 2021. Club officials have decided not to activate it, the report said.
The 35-year-old was suspended for two weeks on Tuesday, L’Equipe added, as he was supposed to practice with his team following a 3-1 defeat at home against Lorient in Ligue 1 on Sunday but instead flew to Saudi Arabia.
The Argentina World Cup winner is banned from playing or training with the team, and his pay will be docked during his suspension.
Messi will miss the upcoming Ligue 1 matches against Troyes and Ajaccio but might return for the match against Auxerre on May 21. He will then be available for the club until the season ends on June 3.
PSG are top of the standings with 75 points from 33 matches, five points ahead of second-placed Olympique de Marseille.