Caballero, a free agent following his release from Manchester City, was looked to have sealed a transfer to Stamford Bridge as a back-up option after Asmir Begovic agreed at £12 million deal with Bournemouth.
Thibaut Courtois will remain Chelsea's first choice and is locked in contract negotiations after rejecting their initial offer, but finding a suitable back up for him may more prove difficult than the Blues expected due to Newcastle's late approach for Caballero.
The Magpies want him to compete for their No. 1 jersey after they were promoted to the Premier League.
The Argentine has also been linked with a return to his first club Boca Juniors, but his agent says it is a straight choice between Chelsea and Newcastle.
"We have some offers from England, he wants to stay in England," Adrian Faija told Goal.
"Newcastle is cold but pretty and the beaches in Brighton are beautiful as well and easily accessible from London.
"There isn't an offer from Boca. To analyse it, first, we need an offer. It needs be real first [before we consider a move to Buenos Aires]."
Caballero is on holiday in his homeland and he will make a firm decision on his future after his post-season break.