Pep Guardiola's club have been one of the big spenders in this summer's transfer market, parting with more than £200m on new faces.
The two-time Premier League champions have already strengthened their defence with three new recruits, but it seems that the manager is not entirely satisfied.
According to Sky Sports News, City have been keeping tabs on Evans for weeks, and talks are underway between the two clubs.
The broadcaster has given conflicting reports, with one of its sources claiming that a bid has already been rejected by the Baggies, while another stating that talks have not yet progressed to that stage.
If Evans were to move to the Etihad Stadium, it could be somewhat controversial given that he spent nine years of his career playing for Manchester United.
The Northern Ireland international left Old Trafford in 2015 to join West Brom after falling out of favour with then-manager Louis van Gaal.