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.
Goal revealed on Tuesday that PSG had remained in contact with the youngster throughout their pursuit of a record-breaking deal with 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.
The Catalan coach has acknowledged that he wants “something more” before the transfer window slams shut on August 31.
City have prioritised a move for Arsenal forward Alexis Sanchez, with the Chilean having entered the final 12 months of his contract at Emirates Stadium.