The former Blackburn Rovers player is expected to end his association with the Merseyside club in the January transfer window after being frozen out by the Pool manager Rafael Benitez.
Argentine veteran Pellegrino is being added as cover for the likes of Jamie Carragher and Sammi Hyppia meaning that Henchoz will be pushed further down the pecking order in the Reds first team.
A number of clubs have expressed an interest in the services of Henchoz, notably the likes of Charlton Athletic and Southampton, but Wanderers boss Sam Allardyce is hoping to keep the player in the North West area.