Mbappe has been in a contract stand-off with PSG amid a desire to join Real Madrid.
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.
As a result, Mbappe was left out of PSG’s touring squad for their pre-season trip to Asia.
He subsequently refused to meet with representatives of Al-Hilal, who made a world record offer to bring him to the Saudi Pro League.
PSG begin their French title defence at home to Lorient on Saturday and it is understood Mbappe will train with the ‘loft’ group rather than the ‘A’ training group, which is players who could feature for the first team.
PSG sources say their most recent attempt to broker a solution to the situation was to offer Mbappe a guaranteed sale clause in his contract for the end of this season. This offer was rejected.
After years of underachievement at Champions League level with their ‘galactico’ model of signing superstar players, PSG are now going down a different path and are understood to be close to completing a deal for Benfica’s Goncalo Ramos.
The 22-year-old scored a hat-trick for Portugal at last year’s World Cup in Qatar and has attracted interest from numerous top European clubs.
PSG are expected to pay 80m euros (£69m) for the forward.