City and Arsenal were both interested in the Northern Ireland international during the previous transfer window, only for the Baggies to keep hold of the defender.
The Express reports that both clubs have retained an interest in the former Manchester United man and are preparing to battle for his signature once again when the window reopens at the turn of the year.
City are keen to add further cover at the heart of their defence, having seen John Stones ruled out through injury to leave Vincent Kompany, Nicolas Otamendi and Eliaquim Mangala as their only recognised senior centre-backs.
However, new West Brom boss Alan Pardew is understood to be desperate to keep Evans at The Hawthorns and will reportedly offer the 29-year-old a new deal in an attempt to convince him to stay.
Liverpool have also been credited with an interest in Evans, who is expected to command a fee of at least £30m.