Premier League footballer Emiliano Sala was on a light aircraft which went missing over the Channel Islands.
The £15m Argentine striker, 28, was one of two people on board the Piper Malibu which lost contact off Alderney in the Channel Islands on Monday night.
Cardiff City, which signed Sala from French club Nantes in a record deal on Saturday, said it was "very shocked".
Guernsey Police said there was "no trace" of the Cardiff-bound flight and his family said they felt "desperate".
Sala's father, Horacio, told Argentine TV channel C5N, he heard the news from a friend.
"I didn't know anything. I couldn't believe it," he said. "I'm desperate. I hope everything goes well."
Meanwhile, John Fitzgerald, chief officer of the Channel Islands Air Search, said the probability of finding anyone alive from the missing aircraft was "reducing very rapidly".
"I think with the sea temperatures and the sea conditions the chances of finding anybody alive are reducing all the time," he said.
"The sea temperatures are very, very cold and just sap the core temperature of anybody in the water very, very quickly."
The plane left Nantes in north west France at 19:15 and had been flying at 5,000ft when it contacted Jersey air traffic control requesting descent, Guernsey Police said.
The plane lost contact while at 2,300ft and disappeared off radar near the Casquets lighthouse, infamous among mariners as the site of many shipwrecks, eight miles (13km) north-west of Alderney.
The force added UK authorities have been calling airfields on the south coast to see if it landed there but there had been no confirmations and a decision about an overnight search would be made at sunset.
A spokesman for the French Civil Aviation Authority said the Piper PA 46 Malibu aircraft was French but had not been registered in France.
"We can confirm Emiliano Sala was on board," he said.
"This morning, the French research started with one French national navy ship and one aircraft. The investigation will determined which authority will take the lead on the research."
Sightings of red flares were reported during a lifeboat and helicopter search, but "nothing of significance was found", a Channel Islands Air Search spokeswoman said.
Police said on Tuesday more than 1,150sq miles had been searched by five aircraft and two lifeboats. The search had resumed after being called off overnight "due to strengthening winds, worsening sea conditions and reducing visibility".
Cardiff Airport confirmed the aircraft was due to arrive from Nantes but a spokeswoman said there were no further details.
Guernsey harbour master Captain David Barker said no distress call had been received and if the search continues into the night it is unlikely to have a good outcome.
"We are looking for any traces of an aircraft, a life raft, persons in the water, life jackets," he said.
The Met Office said conditions were not "too intense" at the time the aircraft went missing but had become wetter and windier later in the evening.
John Fernandez, a reporter for BBC Guernsey, said it was a difficult area to search.
"A number of search vessels are out searching the area. It's known for its strong currents - there are a number of shipwrecks," he added.
"The search area is absolutely massive at the moment. They're searching a number of different spots at the moment - they're not sure whereabouts this plane might have gone down."
Cardiff signed Sala for a club record fee after protracted negotiations with Nantes and he was due to join his new teammates for training on Tuesday.
In a statement, the club's chief executive Ken Choo said training had been cancelled and they were praying for "positive news" for the player and pilot.
He added: "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.
Police tweeted a map of the area which had been searched
"Our owner, Tan Sri Vincent Tan, and chairman, Mehmet Dalman, are all very distressed about the situation."
He has been among the top scorers in France in recent years and had scored 13 league and cup goals this season, third behind Kylian Mbappe and Nicolas Pepe.
Nantes president Waldemar Kita said: "I'm thinking of his friends, his family, I'm still in hope, he's a fighter, it's not over, maybe he's somewhere, waiting for some news that we hope will be positive, we are very touched by all the support received since this morning."
Sala began his playing career at Argentine side Club Proyecto Crecer, before moving to French club Girondins Bordeaux in 2012.
His previous side, Nantes, has postponed its games against Entente on Wednesday and St Etienne on Saturday, according to its match schedule.
The most recent tweet from Sala's account was a picture of him and his former team-mates, captioned "La ultima ciao", or "the last goodbye".
Local journalist Arnaud Wajdzik said the atmosphere in Nantes was "very emotional", and people planned to gather in the town square on Tuesday evening for a vigil.