The family of missing footballer Emiliano Sala are "struggling with very, very few answers about an unexplained loss", a spokesman said.
Cardiff City's signing was on a flight with pilot David Ibbotson, which disappeared over the English Channel.
An official search was called off on Thursday with Guernsey's harbourmaster saying the chance of them being alive was "extremely remote".
However, £280,000 has been raised for a private search to continue.
After Argentine Sala's disappearance last Monday, his sister Romina travelled to Cardiff, before she arrived on Guernsey on Sunday with their mother, Mercedes.
"This is a family that has come from Argentina with this huge shock out of nowhere and is struggling with very, very few answers about an unexplained loss," family spokesman David Mearns said.
He added the family "still have some hope", saying: "They're looking at this as a missing person, a missing plane and until they are satisfied that's the mode that we are in."
Mr Mearns is leading the private search, which he said would entail "more investigative technical searches underwater" at some point.
He said the family had travelled to Guernsey to be near where the plane was last located and to find out about the investigation and what happens next.
They thanked donors for their "exceptional generosity" after £280,000 was raised to pay for a private search.
Two boats hired using the money resumed looking on Saturday.
Mr Mearns said Guernsey authorities were answering all the family's questions about their investigations.
"But as you know locally the search was terminated on Thursday and that was what triggered this private search," he said.
"Today, even as an expert my frame of thinking is alongside with the family's.
"That's what I'm trying to do. But we're trying to give them the best advice that we possibly can. You have to appreciate they don't know the environment, they don't know the geography."
Sala signed for Cardiff City for £15m and he was travelling to the Welsh capital from Nantes, where he had previous played.
High-profile donors to the GoFundMe page include France and PSG forward Kylian Mbappe, former West Ham midfielder Dimitri Payet and Leicester City winger Demarai Gray.
More than 4,000 people have donated to the page.
The initial target of 150,000 euros (£130,000) was met within 24 hours and two private search vessels began to scour the sea again on Saturday.
In a message from the family published on the fundraising website, they said the tragedy goes "far beyond football" and the money would be used "exclusively for research".
A decision was made by authorities to stop looking for the Piper Malibu plane carrying the Argentine and Mr Ibbotson, from Crowle, Lincolnshire, on Thursday after three days of searching land and sea around the islands of Guernsey and Alderney.
Three planes and five helicopters racked up 80 hours combined flying time looking for the aircraft, alongside two lifeboats and passing ships.
The fund was set up on Friday by Paris-based sports agency Sport Cover, which lists Sala as one of its clients.
Guernsey harbourmaster David Barker said on Thursday the chances of survival were "extremely remote".