But City have since snapped up Ederson from Benfica in a £35m deal and Caballero's contract was allowed to run down.
According to reports, Rafa Benitez has made an offer to sign the veteran keeper, in an effort to bolster his squad ahead of the Premier League challenges.
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 hard than the Blues expected due to Newcastle's late approach for Caballero.
We don't imagine it will be any different here, as Thibaut Courtois has firmly nailed down that position between the sticks.
As reported on Sunday, the Blues are not expected to announce his arrival until July 1.
The 35-year-old also had interest from Newcastle United and Boca Juniors in Argentina.
"Newcastle is cold but pretty and the beaches in Brighton are attractive as well and easily accessible from London".
The agent of Argentine goalkeeper Willy Caballero has claimed that his client is keen on staying in the Premier League.
"There isn't an offer from Boca. It needs be real first [before we consider a move to Buenos Aires]".
Conte has been frustrated so far this summer and Caballero could be his first signing since winning the title.
Belgian striker Romelu Lukaku remains the Blues' top target.