The club's all-time leading goalscorer is refusing to sign a year's extension to his contract which ends next summer.
PSG therefore want to sell the France forward now and secure a transfer fee rather than let him go for nothing.
Mbappe, however, has said he wants to remain with PSG for one more year before leaving upon the expiration of his current deal.
He is widely believed to be aiming to join Real Madrid for nothing at the end of the upcoming season.
The striker remains the second most expensive player ever, joining PSG in 2017 in a transfer worth £165.7m. The World Cup winner has scored 212 goals in 260 games since arriving from AS Monaco.
PSG believe the present situation cannot be allowed to continue and for Mbappe to remain as part of their playing group, hence the decision to leave him at home.
Chairman Nasser Al-Khelaifi has made clear his determination to take a hard-line stance over the issue, saying it is "impossible" that Mbappe will be allowed to leave for free in 2024.
It is understood a number of clubs have inquired about Mbappe and PSG would be willing to sell this summer. It is thought unlikely the forward would accept any deal given his preference to join Real next summer.
PSG won Ligue 1 last season, but finished just a point ahead of RC Lens despite their comparatively enormous financial resources, and were knocked out of the Champions League in the last 16 by Bayern Munich.
Manager Christophe Galtier was removed from his position earlier this summer and replaced by former Barcelona, AS Roma and Spain boss Luis Enrique.
Another of PSG's star forwards, Lionel Messi, has already departed this summer. The Argentine, whose country beat Mbappe's France in the final of the World Cup in Qatar last December, has joined Inter Miami in Major League Soccer.#football #sports