The search had taken place since Monday but has now been abandoned.
Sala was being flown to Cardiff after completing a record transfer for the club from Nantes.
On the search ending, Harbour Master Captain David Barker said: “My team have just met to review the search and rescue operation which has been underway since the plane disappeared on Monday night.
“Despite the best efforts of air and search assets from the Channel Islands, UK and France, which has covered an area of approximately 1,700sq. miles – with a significant amount of this searched more than once – and having examined mobile phone data and satellite imagery, we have been unable to find any trace of the aircraft, the pilot or the passenger.
“We reviewed all the info available to us, as well as knowing what emergency equipment was on board, and have taken the difficult decision to end the search.
“The chances of survival at this stage are extremely remote.
“Next of kin have been informed of this development, and my thoughts go out to the family of the pilot at this difficult time.”
Pilot Dave Ibbotson checked himself into Nantes airport in France when he arrived to collect the player and admitted he was ‘a bit rusty’.
The pilot tagged himself at the French city’s airport on Saturday before replying to comments the following day, in which he said he was ‘a bit rusty with the ILS (instrument landing system)’.
When questioned by a friend if that was really the case, Mr Ibbotson replied: “You wanna bet, a little on the high side hehe, better than on the low side.”
The plane carrying Sala disappeared from the radar flying over the English Channel on Monday.
Police had earlier confirmed it had become a recovery operation rather than a rescue mission.