The French champions return to their training base on Monday after their pre-season tour of Japan and South Korea, however, Mbappe is not expected to be on the pitch with his usual teammates.
The PA news agency reports Mbappe will instead be part of the 'loft' training group as his stand-off with the club drags on.
PSG sources remain convinced the player, who is out of contract next summer, has already agreed a free transfer deal with Real Madrid.
Mbappe's management are understood to have refused to engage with an offer from the club to sign a new contract containing a guaranteed sale clause, which would allow him to join another club for a fee next summer.
From PSG's perspective, there is no reason why he would turn down the offer, because it gives him the opportunity to leave when he wants and join the club he wants.
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PSG had given Al Hilal permission to speak to the player after they tabled a world record bid of £259million last month, but Mbappe reportedly refused to even meet with delegates from the Saudi club who had flown to Paris.
Chelsea and Barcelona are understood to be two of the clubs trying to work out a player-plus-cash deal for Mbappe, who was part of France's World Cup-winning squad in 2018 and also one of the stars of the last tournament in Qatar.
PSG kick off their 2023/24 Ligue 1 campaign at home to Lorient on Saturday.
Mbappe joined PSG from Monaco in 2017 on an initial loan deal before making the move permanent in 2018.
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The 24-year-old has 212 goals in 260 appearances for the club and has won 12 trophies with them, including five Ligue 1 titles.
He was due to leave on a free transfer last summer but unexpectedly put pen-to-paper on a bumper new two-year deal with an option to a third.