The Blues have already informed the Portuguese club of their interest with a view to making an official bid for the player’s services in the summer transfer window.
With John Terry in the closing stage of his career and David Luiz heavily linked with a switch to Barcelona, the Stamford Bridge outfit are keen to sign Garay for the 2013/2014 season.
The only problem is that Manchester United have long ago expressed their interest in the experienced centre-back, with the Premier League rivals likely to enter a real bidding war for the Argentine.
Benfica officials see Garay as a key member of the squad, but club’s transfer policy is such that every player has a price.
The 26-year-old, who joined the Eagles from Real Madrid, has made a total of 43 Primeira Liga appearances for Benfica, while also featuring in 17 Champions League matches for the club.