After starting the FA Cup final last season, the goalkeeper’s stock has fallen rapidly this term and he was reduced to being the third choice after Edouard Mendy joined the club last summer.
The 39-year-old has played just once in the Premier League and is now firmly down the pecking orders of goalkeepers at Chelsea.
The Argentine has been considering leaving the club in the winter transfer window in search of more first-team football.
A move to the MLS was mooted and there were also suggestions of other clubs being interested in the experienced shot-stopper.
But Caballero will not be leaving Chelsea before the transfer window closes an hour from midnight tonight.
He is destined to spend the rest of the season behind Mendy and Kepa Arrizabalaga in the Chelsea squad.
The Blues want an experienced back-up in their squad should Mendy or Kepa pick up an injury in the latter half of the season.
He is out of contract in the summer and will be able to leave Chelsea then on a free transfer.
