He is looking to add two new goalkeepers to his squad this summer, after Joe Hart returned to Manchester City.
Adrian also looks set to quit the London Stadium, leaving West Ham's No1 spot clear.
And Pellegrini is looking to bring in Caballero, after growing close during their time at the Etihad.
The ex-City boss bought the 36-year-old to the Premier League from Malaga back in 2014.
PELL TO PAY OUT Manuel Pellegrini to get £75million to reshape West Ham and claims four or five players will make them strong
And Pellegrini is understood to have full trust in the veteran goalkeeper, after time spent working together.
The West Ham chief dropped Hart for the League Cup final back in 2016 in favour of Caballero.
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