Sala and 60-year-old David Ibbotson have been missing since 21 January when their plane disappeared from radar 20 kilometres north of the island of Guernsey.
"We reviewed all the information available to us, as well as knowing what emergency equipment was on board, and have taken the difficult decision to end the search," Guernsey police said in a statement. "The chances of survival at this stage are extremely remote."
Sala, 28, signed for Cardiff City on 19 January after two years with the French club Nantes. He was flying to Cardiff in a United States registered single-engine Piper PA-46 Malibu aircraft.
Police said teams from the Channel Islands, mainland Britain and France had searched an area of 4,400 square kilometres.
However Sala's sister, Romina, pleaded with authorities to maintain the search. "I know in my heart Emiliano is still alive," she said.
"We understand the effort but please don't stop the search. For us, they are still alive. It is difficult to express our feelings at the moment because everything is really hard."
Police said rescuers had spotted a number of floating objects in the water but had not been able to confirm whether these were linked to the plane.