The French club want more than £110 million for Mbappe, who has emerged as one of the brightest talents in world football this season.
It was reported last August that City made a bid of €40m for the then 17-year-old during last summer's transfer window, only to be rebuffed.
The Premier League side have maintained their interest throughout the current campaign and recently made an enquiry about the youngster's availability.
Monaco, however, have quoted what would be a world-record fee for the 18-year-old in the hope of retaining his services for at least another season.
Monaco's vice-president Vadim Vasilyev recently insisted, "We will do everything to keep them" in the face of rumoured interest from Europe's major clubs in youngsters Mbappe, Bernardo Silva and Thomas Lemar.
City are in the market for a new forward this summer and are confident they can prise Alexis Sanchez from Arsenal.
The Chilean would be available for less than half of Mbappe's fee as his contract expires next summer and it is believed he will quit the Emirates Stadium at the end of the season, barring a dramatic change of heart should the Gunners win the FA Cup.
Sergio Aguero is determined to stay at the Etihad Stadium this summer but there remains a possibility that he could yet leave, with Paris Saint-Germain leading the chase for his signature, as revealed by Goal earlier this season.
Aguero was substituted during Sunday's FA Cup semi-final defeat to Arsenal but it is understood he will be fit enough to start Thursday's Manchester derby, though he may have to contend with Gabriel Jesus, who is back in training following a broken bone in his foot.
David Silva was withdrawn earlier than Aguero at Wembley on Sunday and is also hopeful of facing United this week, though he will have further checks over the next two days.