Floating objects have been found in the water, and police on the British island of Guernsey, which sits off the north coast of France, have warned the chances of the passengers surviving were "slim".
As the air search resumed, Argentine media reported that Sala sent a final message before the plane disappeared from radar around 20 kilometres (12 miles) north of Guernsey on Monday night.
"I'm on a plane that looks like it's going to fall apart, and I'm leaving for Cardiff," the 28-year-old said in a WhatsApp audio message.
"If in an hour and a half you have no news from me, I don't know if they will send people to look for me, because they will not find me, you know... I'm so scared," he added.
Sala, who signed with the Premier League club on Saturday from French Ligue 1 club Nantes for a reported fee of 17 million euros ($19.3 million), was flying to Cardiff on a single-engine Piper PA-46 Malibu aircraft.
A 15-hour search Tuesday covering 1,155 square miles (3,000 square-kilometre) in the Channel spotted "a number of floating objects in the water", Guernsey police said.
On Wednesday, they said two planes had resumed searching a targeted area, including around the nearby island of Alderney, based on the theory that the plane might have landed on water and the occupants got into a life raft that was on board.
- 'Fearing the worst' -
In Sala's Argentinian hometown of Progreso, his father Horacio told the press that as "the hours go by and I don't know anything, it makes me fear the worst".
Daniel Ribero, president of the San Martin Athletic Club in the town, told AFP: "These are hours of uncertainty, of much pain and much sadness, waiting for the good news that he is alive."
But one of the rescuers searching for the missing plane admitted they were "fearing the worst".
"The sea temperature is so cold at the moment," John Fitzgerald, chief officer of Channel Islands Air Search, told AFP.
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."
The pilot had requested to lower his altitude shortly before air traffic control in neighbouring Jersey lost contact with the plane, they said.
French civil aviation authorities had confirmed Sala was on board. It is thought there was one other passenger on the aircraft.
The player's mother, Mercedes, told Argentine television channel C5N that the plane belonged to Cardiff chairman Mehmet Dalman.
- Fans hold vigil -
Sala, who had been at Nantes since 2015 and had scored 13 goals in all competitions this season, had signed a three-and-a-half-year contract with relegation-threatened Cardiff subject to receiving international clearance.
Cardiff's executive director Ken Choo said they were all "very shocked" at the news, saying they had expected Sala to arrive on Monday evening ahead of his first day with the team on Tuesday.
"We continue to pray for positive news," he said.
Argentine football legend Diego Maradona said he was hoping the plane had simply gone astray.
"I hope it went to the wrong airport and we find him alive, that's all," he said in an audio message.
"It's a terrible misfortune when such things happen."
Cardiff called off Tuesday's training session, and stunned supporters laid flowers and scarves outside the club's stadium.
With his former teammates in shock, Nantes have postponed their French Cup tie against third-tier side Entente Sannois Saint-Gratien on Wednesday until Sunday.
Hundreds of fans gathered for a vigil in the western French city on Tuesday, placing flowers, scarves and flags on a fountain and chanting the striker's name.
"I still have hope, he is a fighter," Nantes president Waldemar Kita tweeted.
When he signed at Cardiff on Saturday, Sala -- who also has Italian nationality -- said in a statement: "I'm very happy to be here.
"It gives me great pleasure and I can't wait to start training, meet my new team-mates and get down to work."
His last post on Instagram showed him surrounded by Nantes players before leaving. "La ultima ciao (the last goodbye)," he wrote.
Sala began his career at Bordeaux in 2010 and had loan spells at other French clubs including Orleans, Niort and Caen.
He joined Nantes in 2015 for one million euros and had scored 42 Ligue 1 goals in three and a half seasons.