The Citizens are ready to capitalise on the Hammers' interest in Joleon Lescott, by offering the centre-back as part of a player-plus-cash deal for the England U21 international.
Morrison is a former Manchester United player, who left Old Trafford in January 2012, following a fall-out with Sir Alex Ferguson.
He has been one of the few positives at Upton Park this season, following a series of impressive performances for Sam Allardyce's relegation-threatened side.
In fact, the London Metro reported last month that new Red Devils boss David Moyes was considering a bid to bring Morrison back to Manchester.
The 20-year-old has been linked with a move away from east London in recent weeks, but it's the first time that Manchester City have been credited with an interest in his services, as Manuel Pellegrini weighs up a last-ditch attempt to lure him to the Etihad Stadium.