BBC Sport states that the Citizens are keen on bringing the Northern Irishman international to the club, having held discussions during the last few weeks with the Baggies, but that their initial offer for the 29 year-old has been turned down.
Interest in Evans remains
As West Brom embark on their eighth-consecutive Premier League campaign, Evans was handed the captain's armband in recent months in an attempt to ward off potential suitors, as Tony Pulis aims to further consolidate his side's place in the top flight.
West Brom have already rejected a £10m offer for the defender from Leicester City over the summer and after Evans help guide the Baggies to an opening day win over AFC Bournemouth on Saturday, Pulis will been desperate to hold on to his skipper.
It was only 12 months ago that the club rejected the advances of Arsenal for the defender.
Despite the signing of Ahmed Hegazi over the summer and with vice-captain Gareth McAuley struggling with injury, Craig Dawson remains the club's only other available player to fill the void.
Guardiola keen to boost ranks
Evans, who played 198 games for Manchester United before joining West Brom in 2015, has two years left on his existing deal at The Hawthorns, having scored three goals in 61 appearances.
City boss Pep Guardiola stated last month, that he was hoping to sign another defender before the transfer window closed, as the club look to juggle European and domestic competitions.
The Spaniard is thought to be keen on a deal for the centre-back, but faces fierce competition for places with opposite number Vincent Kompany, Nicolas Otamendi and John Stones to contend with at the Etihad this term.