The Argentine striker was one of the victims of Dundee's fall into administration, as he had his contract terminated along with a host of other first team regulars.
Caballero's former Dundee team-mate Georgi Nemsadze joined the Fratton Park outfit for a trial last week and it would appear Pompey boss Harry Redknapp was also alerted to the Argentine's availability.
A host of clubs are monitoring his situation, but Pompey have jumped to the head of the queue by putting him through his paces in a trial.
"They (Caballero and Nemsadze) are training with us but that's as far as things have gone at the moment," confirmed Redknapp.
Redknapp is desperate to bolster his ranks in order to stave off the threat of relegation, with Caballero being the fifth player to join the club on trial following the earlier arrivals of Nemsadze, Adrian Ilie, Nenad Miskovic and Maris Verpakovskis.
The Pompey chief is aware he needs to bring in fresh faces, as he said: "If you look at Leicester they've not spent a lot of money but they have got eight or nine players more than us who can all play at this level.
"You think you've got it conquered and then you lose a couple."
