During the summer, both clubs were keen to sign the Northern Ireland international after he had helped the Baggies sit in eighth place in the Premier League table for much of the campaign.
Evans eventually stayed at The Hawthorns and remains a key part of Alan Pardew's side but according to The Sun, the Gunners and City are ready to launch bids in January.
Pardew is ready to offer Evans a new contract with a pay-rise, but Arsenal boss Arsene Wenger is allegedly hoping to lure the 29-year-old to the Emirates Stadium with the guarantee of first-team football.
As far as City are concerned, Pep Guardiola sees Evans as an alternative to Vincent Kompany and while starts may be more limited in the North-West, the former Manchester United man is said to be keen on joining the top-flight leaders.
Evans has 18 months remaining on his contract at West Brom.