Or at least they thought he had been convinced.
The suggestion from French media is that PSG might have gone even further with the signing-on fee, plus offering other advantages Real Madrid could not match (more control over sporting decisions, future deals with Qatar, etc).
PSG's proposal is less dramatic than it sounds, because it is something that happens with big stars anyway. They do get asked about managers and big transfers, especially at PSG, where the influence of the manager is smaller than at other places.
While his mum and dad are his closest advisors and deal with his affairs, with the close help of their lawyer, Delphine Verheyden, ultimately the decision was completely up to him and there has been a significant change in attitude.
The link between this year's Qatar World Cup and the Qatari owners of PSG is a clear one. The pressure from Qatar has gone to the political authorities in France and even French president Emmanuel Macron got involved in putting pressure on Mbappe to stay.
Not so long ago I was getting very clear indications from the PSG entourage that nothing could change his mind about leaving. Even when there was talk of one of his idols, Zinedine Zidane, coming in as manager, it was said that would not be enough to convince him to remain in Paris.
But all those impressions changed over the past few weeks and the PSG players started to think he was staying.
From a purely footballing point of view, one element Mbappe might have considered is whether he can win the Ballon d'Or at PSG. For that to happen, he would need to have a near-perfect Champions League campaign with PSG, scoring 10 goals or more and winning the tournament, fighting with the likes of Real's Karim Benzema, Erling Haaland, now at Manchester City, and Dusan Vlahovic, at Juventus. It is harder to win an individual trophy at PSG.
But it may well be that he still ends up at the Bernabeu one day, of course. His age is not an issue because, at 23, he knows he can stay for a couple of years at PSG and help them win that elusive Champions League trophy, then go to Madrid and have five or six years there at his absolute peak.
For now, for Madrid, it is an embarrassing conclusion to their pursuit of a player who would have been the first cast-iron Galactico since Ronaldo's departure in 2018, or you could argue the first one to arrive since Eden Hazard joined in 2019. They will have to explain it to their fans somehow.
The club's president, Florentino Perez, has been exposed by this given the months of confident briefing from the Madrid side that a deal would happen, and waiting for Mbappe's arrival has slowed down their squad planning in other areas.
We will probably hear again that this is confirmation Madrid and other La Liga teams can't compete with what they call 'state clubs' (La Liga president Javier Tebas has already mentioned that last week). Real Madrid will try to make it clear the club did all they could to get him.
Now Mbappe's decision has been made, you might think it would be greeted as universally great news by PSG supporters, but remember they have whistled their Paris-born striker this season.
Of course the fans will celebrate but there is such a disharmony outside the club that PSG will have to do much more to keep everyone happy. Big decisions are still required, perhaps finding a new manager and director of football, though Mbappe has got a very good relationship with current boss Mauricio Pochettino.
For now, they have done enough to satisfy Mbappe and they will hope that is the catalyst for them to finally win the Champions League they crave so much.
Guillem Balague writes a regular column throughout the season and also appears every Thursday on BBC Radio 5 Live's Football Daily podcast, when the focus is on European football.