Guernsey Police have said the chances of finding Emiliano Sala alive are "slim" if the plane carrying the Cardiff striker over the English Channel landed on water.
The French Civil Aviation Authority said Sala was aboard a light aircraft that disappeared from radar en route from Nantes to Cardiff on Monday evening.
Guernsey Police said the Piper PA-46 Malibu, a single turbine engine aircraft carrying two people, departed Nantes at 7.15pm for the Welsh capital and was flying at an altitude of 5,000ft.
On passing Guernsey it "requested descent", but Jersey air traffic control (ATC) lost contact with the plane while it was flying at 2,300ft.
After a 15-hour search from rescue teams, which covered an area totalling 1,155 square miles, Guernsey Police revealed that "a number of floating objects" were seen in the water, but they were "unable to confirm whether any of these are from the missing aircraft".
The search and rescue operation - which included multiple air and sea assets from the Channel Islands, UK and France - was suspended for the day at 1700 on Tuesday and will resume at sunrise on Wednesday morning.
A statement posted on the official Twitter account of Guernsey Police said: "We have found no signs of those on board. If they did land on the water, the chances of survival are at this stage, unfortunately, slim."
Earlier on Tuesday, Cardiff's executive director Ken Choo expressed his shock and distress at the news.
Sala, 28, was on his way back to Wales after saying goodbye to his Nantes team-mates on Monday night.
Choo said in a statement: "We were very shocked upon hearing the news that the plane had gone missing. We expected Emiliano to arrive last night into Cardiff and today was due to be his first day with the team.
"Our owner, Tan Sri Vincent Tan, and chairman, Mehmet Dalman, are all very distressed about the situation.
"We made the decision first thing this morning to call off training with the thoughts of the squad, management staff and the entire club with Emiliano and the pilot.
"All of us at Cardiff City FC would like to thank our fans, and the entire footballing family for their support at this difficult time.
"We continue to pray for positive news."
Sala had signed a three-and-a-half year deal with the Welsh club after scoring 12 Ligue 1 goals in 19 appearances this season.
Choo described Sala as a "great person" and revealed he had been "so happy" to sign for Cardiff.
He said in an in-house TV interview: "You could see from his face he is so, so happy to be here and ready to start.
"Words cannot describe the look on his face when he met us, we walked him around the ground, he was absolutely ready to give it a go.
"We really feel sad to hear of this news because we met such a great person."
Choo revealed Sala had described joining the Bluebirds as "one of the best days of his life".
Cardiff have been in contact with Sala's family as they wait for news.
Choo said: "We are waiting for (French aviation authorities) to inform us. We are trying to communicate with them, the agent of the player and the family.
"We like to reach out to the family because it's a very tough time.
"At this point in time we just want to know if he and the pilot are OK."
Cardiff City Supporters Club spokesman Vince Alm said: "The reaction is one of shock, devastation and concern.
"You just think of a young man making a career move that he had probably dreamed of all his life. Hope is obviously fading as time goes on."
Nantes president Waldemar Kita added on the French club's website: "I'll always have hope, he's a fighter. It's not over, maybe he's somewhere."
Nantes' Coupe de France clash with third-tier Entente Sannois, scheduled for Wednesday evening, has been postponed until Sunday while their Ligue 1 fixture against St Etienne - originally due to take place on Saturday - has been moved to Wednesday, 30 January.
Sala, a native of Santa Fe in Argentina, played at youth level for Club Proyecto Crecer in his home country before being snapped up by French club Bordeaux in 2010.
He was then sent out on a series of loans to Orleans, Niort and Caen and, after failing to make more than a handful of appearances for Bordeaux, joined Nantes in 2015.
It was in Brittany that his career began to flourish.
Sala's hat-trick against Toulouse in October 2018 was the first by any Nantes player in Ligue 1 since 2006.
Cardiff signed the forward in a deal reportedly worth in the region of £15million, breaking the previous record of £11million paid for Gary Medel in 2013.