Silva flew into Manchester on Thursday night and arrived at City's Etihad Campus training ground to complete a medical on Friday.
It is believed City and Monaco struck a deal just days after the close of their respective league campaigns and the French club allowed Silva to fly to Manchester in the middle of this week.
Silva will sign a five-year contract at the Etihad Stadium once he has successfully completed his medical.
City staff were said to be laying the groundwork for a major announcement late into Thursday evening.
The club released four players on Thursday, including three full-backs, and they are also believed to be very close to signing Kyle Walker from Tottenham, while Silva's Monaco team-mate Benjamin Mendy is also a target and could follow the 22-year-old to Manchester.
Monaco are looking for replacements for both Silva and Mendy, with Aston Villa left-back Jordan Amavi one possible recruit.
But it appears as though Silva will be the first one through the doors at the Etihad Stadium this summer.
City are determined to get their business done early having been made to wait for certain key signings ahead of Pep Guardiola's first season in charge.
John Stones did not arrive until just before the Premier League season started while Claudio Bravo only joined after the first international break of the season.
But Guardiola is also keen to add a dynamic attacking midfielder to his ranks, despite already boasting Kevin De Bruyne, David Silva and Ilkay Gundogan, who is hoped to be fit for the start of next season.
Additional reporting by Loic Tanzi.