The Nerazzurri are also mulling a bid for Chelsea's John Obi Mikel as they look to overhaul their squad for the 2014-15 Serie A season.
The 27-year-old has fallen down the pecking order at the Etihad Stadium this season, with Manuel Pellegrini preferring to start Fernandinho and Yaya Toure in the two holding midfield slots in his starting XI.
Inter sees the former Benfica star, who has started just two league games since Jan. 18, as a primary transfer target as it strives to get back in the Serie A title picture following a period of change at the club.
Chelsea midfielder John Obi Mikel is also viewed as a realistic target as owner Erick Thohir looks to make further progress in the transfer market having already secured the free-transfer signing of Nemanja Vidic from Manchester United.
Inter is, however, more confident of acquiring Garcia, who, despite still being considered an important member of the first-team squad by Pellegrini, could be allowed to leave for the right price.
Walter Mazzarri's Inter could also face competition from Serie A rival Napoli for the onetime Real Madrid man, while City will be reluctant to do business for less than the 16 million pound fee it paid to sign him from Benfica back in 2012.