Another reason why PSG might try so hard is that they're lacking the required number of homegrown players for the Champions League.
So far they have Areola (GK), Descamps (3rd GK if not loaned out), Kimpembe, Kurzawa, Rabiot, Nkunku and Matuidi if Aurier and Ben Arfa leave. The closest youngsters to the first team have either been sold (Augustin and Sabaly) or loaned (Ikoné, Robail, Bahebeck, Pereira de Sa) while a few others should be loaned soon (Georgen, Edouard and Callegari). Some of their hottest prospects have been "stolen" by other clubs (Fodé Ball Touré by Lille and Zagadou by Dortmund), so there is no one left ready to step up.
They need at least one homegrown player if Aurier and Ben Arfa leave while Matuidi stays. And the later is closer to leaving than staying, so if Matuidi leaves they could be forced to add a pure prospect (Diaby or Dagba ?) who is not really close to the first team.
This said, I haven't heard M'Bappé demanding anything from Real Madrid. But it would make sens from him in private to pay attention to his game time in a WC year at 18 and give priority to Paris.