The Spaniard is reportedly undergoing a medical with the Russian club and has already been pictured wearing a Zenit shirt.
The proposed move, thought to be worth around £12million, would end a two-year spell at the Etihad Stadium for Garcia, who joined from Benfica for £15.8million.
Garcia, 27, was signed under former manager Roberto Mancini but never became a regular starter for the Italian or his successor Manuel Pellegrini.
His departure would follow the £10million exit of fellow midfielder Jack Rodwell to Sunderland earlier this month.
City effectively already have a replacement for Garcia in the squad having signed Fernando from Porto in June.
Eliaquim Mangala, Willy Caballero, Frank Lampard, Bruno Zuculini and Bacary Sagna are the other new faces in the champions' squad ahead of the new season.
City begin the defence of their Barclays Premier League crown at Newcastle on Sunday.
This week has also seen the City key pair of captain Vincent Kompany and playmaker David Silva sign new five-year contracts.
Samir Nasri and Aleksandar Kolarov agreed fresh terms earlier this summer.
Now striker Edin Dzeko, who is in the final year of his current deal, has suggested that he could be the next to re-sign.
The 28-year-old, signed from Wolfsburg for £27million in 2011, has previously spoken of his desire to stay and now it seems negotiations with the club are progressing well.
The Bosnia international, who scored 26 goals last season, told German magazine Kicker: "We are currently talking about a new contract.
"It looks very good in terms of staying here a bit longer.
"I have been here for nearly four years now, and feel better and better
I will give my all to show what I can do.
"The second half of last season was the best I had in my entire time here, and I want to draw on that.
"I want to get better every year, to score even more goals
I am 28 - my best time is now."
Source : PA
Source: PA