The deal, reported to be worth up to £50million, is set to be completed by the end of the week, Press Association Sport understands.
The Brazilian defender worked under City boss Pep Guardiola at Barcelona and had been expected to follow him to Manchester but instead joined Paris St Germain.
Guardiola has been looking to bolster the City rearguard after seeing veterans Pablo Zabaleta, Bacary Sagna and Gael Clichy all released at the end of last season.
Walker, 27, will bring with him the experience of more than 180 Premier League appearances for Spurs, whom he joined from Sheffield United in 2009, and is expected to join up with the rest of the City squad for next week's tour to the United States.
Following Walker's departure, Spurs are likely to give 26-year-old Kieran Trippier, who made his full England debut against France last month, an extended run in the side.
Monaco manager Leonardo Jardim has defensive cover in place following the £12million signing of Terence Kongolo from Feyenoord, which could pave the way for Mendy's proposed big-money switch to the Etihad Stadium.