The Gunners face a fight with a number of clubs for a player rated one of the best in his position in the Spanish top flight.
They mention a fee of £7 million being mooted for the player, who was part of the Spanish club's Champions League run in 2012.
However, there is more than one European giant in the market for Caballero, with Atletico Madrid lining him up to replace Thibaut Courtois should the Belgian return to Chelsea next year.
The Chilean is known to be a big fan of his former number one, and with Costel Pantilimon departing Eastlands this summer, there is certainly room for another top class goalkeeper to come in to keep Joe Hart under pressure to perform.
It may well be that Arsenal's ability to recruit Caballero may well depend on Pellegrini's interest in the player.
The Argentinian, who has never featured for the national team despite several years of impressive performances in Spain, already turned out for one Arsenal side earlier in his career.
Caballero had a loan spell at Argentinian Primera Division side Arsenal de Sararndi in 2006, away from Elche, where the stopper played for 7 years before his switch to Malaga in 2011.