Search and rescue efforts resumed for a third day early on Thursday after the Piper Malibu aircraft with Sala and pilot David Ibbotson on board went missing en route to the Welsh capital on Monday .
But Guernsey Police confirmed that following an extensive operation covering approximately 1,700 square miles around the Channel Islands, no trace of the plane, pilot or passenger had been found.
Harbour master captain David Barker said in a statement the search would therefore cease as "the chances of survival at this stage are extremely remote".
However, Sala's family believe it is too soon to stop looking and were later backed by a statement made on social media by Nantes, Sala's former club, who urged the search to continue for his loved ones' sake.
"FC Nantes learned of the abandonment of the search for the missing plane. They cannot stop," the club said in a statement posted to their official Twitter account.
"The Club and its supporters are demanding that the search to find Emiliano Sala continues, for his family and for his relatives.
"Together, for Emi!"
Le FC Nantes a appris l’abandon des recherches de l'avion disparu.— FC Nantes (@FCNantes) January 24, 2019
Celles-ci ne peuvent s’arrêter. Le Club et ses supporters demandent avec force que les recherches pour retrouver @EmilianoSala1 continuent, pour sa famille et pour ses proches.
Ensemble, pour Emi !#PrayForSala pic.twitter.com/YOjjnoxt9H
Sala's family voiced confusion over the decision to halt the search and hoped the authorities would place themselves in their shoes.
"I'm very confused," Sala's sister Romina said to ESPN . "The only thing that I want is that my brother and the pilot be found.
"We ask them [the authorities] to put themselves in our place, in the hearts of the relatives.
"Please, don't stop searching. I know that they are alive and they are waiting for us."
Sala's father Horacio also urged Guernsey Police to reconsider their decision.
"We are asking to please keep looking for him," he said to TyC Sports.
"We can't believe that they are cancelling the search. I ask that [they] please continue the search.
"It can't be that a plane disappears and there is no trace of anything."
3.15pm Update.— Guernsey Police (@GuernseyPolice) January 24, 2019
Please read the attached statement.
Unless there is a significant development, there will be no further updates pic.twitter.com/jbEIFMB3zi
Cardiff chairman Mehmet Dalman stated Sala made his own travel arrangements, while Mark McKay – an agent involved in brokering the player's move to the Bluebirds – confirmed he organised the flight but denied the missing aircraft was owned by him or his family.
Nantes supporters held vigils in the striker's honour in the French city, while their scheduled Coupe de France fixture against Entente SSG was postponed.