"I'm on a plane that looks like it's going to fall apart," the rising star said in a rambling WhatsApp audio message from on board.
Police earlier said rescuers had spotted "a number of floating objects in the water" but had not been able to confirm whether these were linked to the plane.
British media said the pilot Ibbotson was a 60-year-old married father of three who lived in Scunthorpe in northern England.
Football agent Mark McKay confirmed Thursday he was involved in making the travel arrangements for Sala between France and Wales through the player and his agent Meissa N'Diaye.
"I began to look into arranging a private flight to take him to Nantes on Saturday morning," he told Britain's Sky Sports News.
"That evening, it was confirmed a plane was available to fly Emiliano on Saturday which could remain in Nantes until he was due to return to Cardiff.
"I have been in contact with officials from Cardiff and the player's agent over these difficult past few days and will continue to do so."
In Sala's Argentine hometown of Progreso, his father Horacio told the press on Tuesday that the wait for news "makes me fear the worst".
The striker, 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.
Flowers and scarves were laid outside the club's stadium.
Tributes were also paid to Sala at several French Cup matches this week, while his former Nantes teammate Yacine Bammou raised his hands towards the sky in an emotional celebration after scoring for Caen on Wednesday.