Guernsey Police say that as of yet there is "no trace" of the aircraft which last made contact with air traffic control at an altitude of 2,300ft.
The search for the Piper Malibu jet, which had two people on board, was resumed this morning involving RNLI teams from Aldnerney and Guernsey along with the Coastguard and French rescue teams.
Conditions were treacherous during the search with rough seas, heavy rain and gusts forecast to reach up to gale-force eight.
HM Coastguard said the disappearance was not in the United Kingdom search and rescue area, but it had sent two helicopters to help.
Club chief executive Ken Choo said: "I'm sure all Cardiff City fans will join me in that and we can look forward to seeing our record signing in a Bluebirds shirt".
Cardiff City chairman Mehmet Dalman said the club was "very concerned" by news of the plane's disappearance.
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French media are reporting that it has been confirmed that the Argentine was on board the single engine aircraft which took off from Nantes at 7:15pm local time.
Sala had scored 12 league goals in 19 appearances for Nantes in France's Ligue 1 this season before switching this week to Cardiff.
The flight, which had one other person on board, left the city of Nantes in northern France on Monday night with Cardiff its intended destination. The aircraft was flying at 5000 feet.
The statement added: 'The aircraft on passing Guernsey requested descent. Jersey ATC lost contact whilst it was flying at 2300 feet.
Sala, 28, who had been at Nantes since 2016 and had scored 12 league goals this season, had signed a three-and-a-half-year contract with relegation-threatened Cardiff subject to receiving worldwide clearance.
Helicopters from HM Rescue have helped with the search - despite the fact the disappearance was not in the United Kingdom search and rescue area.