PSG had been linked with a €180 million approach for the France international, but have now denied they will make an official bid due to Financial Fair Play restrictions.
It is reported that the club was in contact with the teenager throughout the massive deal from Barcelona.
Club president Nasser Al-Khelaifi put in a personal call to Mbappe during the those discussions, assuring him that he remained on their radar.
PSG have, however, already been busy this summer adding the likes of Neymar, Dani Alves and Yuri Berchiche to their ranks and will not be tabling a bid for another high-profile addition.
Premier League title hopefuls Manchester City do remain keen on securing a deal for the 18-year-old, but they are unwilling to pay his asking price at present.
Given that PSG and Real Madrid are also reluctant to meet Monaco’s demands, it is understood that Pep Guardiola still fancies his chances of getting a deal done.