Relations between Mbappe and PSG have been tense since the French forward said last month he would not renew his contract which expires at the end of next season, when he could leave Paris for free.
PSG President Nasser Al-Khelaifi has said they will not let him go for free after the club spent 180 million euros to sign him.
According to media reports the Parisian club will put up the 24-year-old for sale as of now as they believe he has already agreed on terms to join Real Madrid for free next summer.
PSG representatives did not immediately reply when contacted by Reuters for comment on Friday.
PSG have won nine of the last 11 Ligue 1 titles, but the team and Mbappe have been frustrated with their performances in the Champions League - a trophy the Parisian club have never won despite all their investment in the squad.
PSG went out in the round of 16 this year when they were beaten by Bayern Munich, failing to score in both legs. Mbappe was injured for the first leg and said they were "helpless" in the second.
Brazilian forward Neymar, another big name tipped to leave the club, has been included in coach Luis Enrique's squad set to play against Cristiano Ronaldo's Al Nassr on Tuesday in Japan.
PSG will also face Japan league's Cerezo Osaka and Serie A side Inter Milan before travelling to South Korea to take on Jeonbuk Motors.