The Northern Ireland international only left Manchester United in 2015 but is now a potential target for Premier League rivals City.
Pep Guardiola is looking for an extra centre-back after allowing Aleksandar Kolarov to join Roma in the summer and with Eliaquim Mangala and Jason Denayer reportedly surplus to requirements.
Sources have told ESPN that the City boss would prefer to add an English or homegrown defender to his squad.
They have been scouting Middlesbrough's Ben Gibson but the Championship side reportedly want around £30 million for their 24-year-old centre-back.
The Daily Telegraph has reported that City had an £18m bid plus add-ons rejected last week.
The 29-year-old, who has recently been made captain at the Hawthorns, was also a target for Arsenal last summer.
Evans was a boyhood United fan and joined the club as a schoolboy and went on to win three Premier League titles and two League Cups during his time at Old Trafford.
However, former United manager Louis van Gaal told him he did not figure in his plans at Old Trafford and he completed a £6m switch to West Brom.