The latest Southampton transfer news, views and rumours.
Their report claims the ex-Manchester City man could be on his way out of Zenit after their Champions League exit, with St Mary's a possible destination.
Garcia endured a relatively unsuccessful spell at Manchester City from a personal point of view but was part of last season's Premier League-winning side.
Meanwhile, Southampton boss Ronald Koeman has hailed 20-year-old midfielder James Ward-Prowse after his return to training following a long-term injury.
“Having James back is good news because I like him a lot as a player. His attacking threat gives us more chances to play," he told reporters.
“He has a fantastic set-piece delivery, he started the season as a first-team player and it is always good to have that kind of player ready to return.
“Thursday was his second full training session, and he completed everything. It was a good moment because he was not afraid. You need to have it in your mentality that the injury is not there. You need to play confidently and not fear the injury.”