The England left-back is on Pep Guardiola’s radar after another solid season on the south coast.
And City are desperate to bring in new full backs this summer.
Benjamin Mendy was understood to be City’s first choice left-back but Monaco are stalling on the bid.
City have already landed Bernardo Silva from the French side but may now miss out on Mendy.
Sky Sports report that City have now turned their attention to former Chelsea defender Bertrand and have already agreed parts of the deal.
It is claimed Bertrand would more than double his current £55,000 a week wages at the Etihad.
City are also hoping to land Tottenham defender Kyle Walker and are expected to close in on a deal after England face Scotland on Saturday.
Guardiola is overhauling his squad this summer following a third-place finish in his first season.
Goalkeeper Ederson will join from Benfica for £35m shortly and the spending could top £300m.
Alexis Sanchez remains a target although Bayern Munich are also in the race.
