The Citizens are preparing to offload their Spanish midfielder in the summer, with Manuel Pellegrini unconvinced by his abilities.
It is understood that a deal for Argentine youngster Bruno Zuculini is already in place, but City are keen to lure a holding player with more experience in as well.
Wanyama has emerged as a target with the Kenyan enforcer having been impressive for the Saints this term.
The Hampshire club lured him south of the border from Celtic last year, despite there being rumoured interest from the likes of Liverpool, Manchester United and Arsenal at the time.
The burly ace encapsulated Southampton’s early season form, and is believed to have caught Pellegrini’s eye in the process.
PSG’s Blaise Matuidi is also an option, while Fernando of Porto – whom they failed with a deadline day swoop for – is another target despite him having recently signed a new contract at the club.
Garcia is likely to be shipped out – with Napoli interested – but City may have to take a significant hit on the £15.8m fee they paid Benfica for his services in 2012.