City had a £18m (€19.8m, $23.2m) bid knocked back earlier this week but, according to the Mirror, they are ready to up their offer to £22m in a bid to secure the Northern Ireland international, who could almost double his wages to £140,000-a-week.
Despite spending over £200m on players so far this summer, Pep Guardiola is determined to strengthen his defensive options and sees Evans as the perfect player to provide cover for Vincent Kompany, John Stones and Nicolas Otamendi.
However, Guardiola will first have to find a buyer for Eliaquim Mangala, who is reportedly on Inter Milan's radar. Arrived from Porto in the summer of 2014, the France international has failed to establish himself in the Premier League and spent last season on loan at Valencia. City are believed to want approximately £30m for the 26-year-old, who arrived for a reported £31.8m transfer fee, which then rose to around £42m due to costs as a result of Mangala's split ownership at Porto
Signing Evans would also allow Guardiola to add a home-grown or 'locally-trained' player to comply with Premier League and Uefa regulations on squad compositions. City are not the only Premier League club in the race for Evans, with Leicester City also understood to be keen to sign the former Manchester United centre-back, who has two years left on his deal at The Hawthorns.
Evans came up through the ranks of United's youth system before making his way into the first team in 2006. He spent his initial years away from the club on loan and on his return, was a regular figure in the Red Devils' back four.
He won three Premier League titles, two league cups and one Fifa Club World Cup under Sir Alex Ferguson's guidance, before Louis van Gaal deemed Evans surplus to requirements and allowed him to join West Brom in 2015 for £6m.
However, former United captain Bryan Robson questioned the club's decision to allow Evans, who played 198 times for United, to leave Old Trafford.
"Jonny Evans is a real good player. I was surprised when we allowed him to leave, especially as I think the fee was £6m to go to West Brom," Robson told talkSPORT on Thursday (17 August).
"There is no way I would have allowed Jonny Evans to leave this football club.
"He is a great lad, he is a really honest boy, he works really hard in training and he has done a great job for West Brom. That's up to West Brom and Manchester City whether that sort of deal happens. All I can say is if you are manager of any football club, Jonny Evans is the type of character that you would want in your football club."