The 28-year-old Argentinian striker was on a Piper PA-46 Malibu, with British pilot David Ibbotson, which disappeared on January 21, just days after he signed for Cardiff City from FC Nantes in a record £15m deal.
The plane had left Nantes in France for Cardiff at 7.15pm last Monday and after requesting to descend, lost contact with Jersey air traffic control over the English Channel.
An official search operation was called off on Thursday as Guernsey’s harbour master Captain David Barker said the chances of survival after such a long period are “extremely remote”.
Shipwreck hunting expert David Mearns is understood to be assisting the family in a private search.
US-born Mearns is a marine scientist, author and explorer based in the UK, who claims to have located 24 major shipwrecks during his career.
It was reported last week that Ibbotson’s pilot’s licence will form part of the investigation into the plane’s disappearance.