City have had a £52 million (€57m) bid accepted for Mendy following weeks of negotiations, a deal which will make him the most expensive defender in history.
That comes after Madrid agreed to sell Danilo for £26.5m (€30m) earlier this week.
City had been wary of competing interest from Chelsea in both players, but now believe they will get their men.
Danilo will join up with his new team-mates in Los Angeles in the coming days, and could even make his debut against his former club on Wednesday.
Madrid have been training in LA ahead of the International Champions Cup match, while City flew into California on Friday.
Goal reported in June that the Blues made an enquiry over the Brazilian towards the end of last season, but were informed he did not want to leave Madrid.
But while City pursued and subsequently missed out on Dani Alves, who left Juventus, the Italian club convinced Danilo to replace his compatriot in Turin.
The Bianconeri eventually cancelled the deal, however, leaving Danilo looking for a new club while City hunted for a new right-back.
Mendy, however, has been one of their priority targets for many months.
The Premier League side agreed terms with the France international several weeks ago, as reported by Goal in the aftermath of Bernardo Silva's signing.
Monaco let Silva leave for £43m but dug in their heels for Mendy. City knew the initial asking price was £40m at the end of May but attempted to negotiate that figure down.
But following the collapse of the Alves deal and the subsequent decision to spend an initial £45m, rising to £50m, on Kyle Walker, Monaco upped their asking price and asked for at least what Spurs received for Walker.
With pre-season now well under way and following Aleksandar Kolarov's unexpected request to join Roma, City agreed to meet the French club's demands on Friday evening.
If both deals are completed as expected, City's summer spending will top £200m, having already signed Silva, Walker and Ederson.