But City have since snapped up Ederson from Benfica in a £35m deal and Caballero's contract was allowed to run down.
Chelsea are in the market for a new back-up goalkeeper to first-choice shot-stopper Thibaut Courtois after the club sold Asmir Begovic to Bournemouth in a deal worth almost £10million last month.
And, with the Northern Echo, claiming that Benitez is looking out for a new 'keeper, and could even be open to selling Darlow, it appeared that Caballero was the first name in the frame.
As reported on Sunday, the Blues are not expected to announce his arrival until July 1.
Conte also wants the club to move quicker when it comes to bringing in new players - yet the board are standing firm, causing a rift between the club and manager.
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.
Adrian Faija said: "We have some offers from England, he wants to stay in England".
He added: "There isn't an offer from Boca".
It looks though Chelsea are finally off the mark, and we hope that this is just the first of many signings we are set to make this summer.