That is according to The Sun, who claim City are willing to pay a world-record fee for the striker, who only moved to PSG for a permanent £160m figure this summer.
Pep Guardiola is said to be a huge admirer of Mbappe, and a move could be made possible by the fact that PSG could be investigated for alleged Financial Fair Play breaches after spending £200m on Neymar on top of the fee paid for Mbappe.
The transfer would also depend on Sterling’s future being resolved.
The England international is yet to sign an extension to his current contract, which expires in 2020, and Real Madrid have been linked with him recently.
City are reluctant to let Sterling leave, but if he does exit that could pave the way for World Cup winner Mbappe to join.
Meanwhile, City are said to be among a group of Premier league clubs that sent scouts to watch Lazio’s Sergej Milinkovic-Savic last week.
The Mirror report that City – along with Liverpool and Spurs – watched Milinkovic-Savic score in Lazio’s 4-1 win over Genoa.
Manchester United have been heavily linked with the Serbian midfielder, but did not make a move during the summer transfer window.
Lazio are said to be confident the 23-year-old will sign a new contract, with his current deal running out in 2022.