Smoke was detected in the toilet and the aircraft's electrics, just minutes before the signal was lost, according to data published on air industry website the Aviation Herald.
However, there has been no official confirmation of the data.
Flight MS804 was en route from Paris to Cairo with 66 people on board.
The Aviation Herald said it had received flight data filed through the Aircraft Communications Addressing and Reporting System (ACARS) from three independent channels.
It said the system showed that at 02:26 local time on Thursday (00:26 GMT) smoke was detected in the Airbus A320 toilet.
A minute later - at 00:27 GMT - there was an avionics smoke alert.
The last ACARS message was at 00:29 GMT, the air industry website said, and the contact with the plane was lost four minutes later at 02;33 local time.
ACARS is used to routinely download flight data to the airline operating the aircraft.Philip Baum, the editor of Aviation Security International Magazine, told the BBC that technical failure could not be ruled out.
"There was smoke reported in the aircraft lavatory, then smoke in the avionics bay, and over a period of three minutes the aircraft's systems shut down, so you know, that's starting to indicate that it probably wasn't a hijack, it probably wasn't a struggle in the cockpit, it's more likely a fire on board.
"Now whether that was a technical fire, a short circuit, or whether it was because a bomb went off on board, we don't know," he added.
Greece earlier said that radar showed the Airbus A320 had made two sharp turns and dropped more than 25,000ft (7,620m) before plunging into the sea.
Egypt has said the plane was more likely to have been brought down by a terrorist act than a technical fault.
However, there has been "absolutely no indication" so far as to why the plane came down, French Foreign Minister Jean-Marc Ayrault said on Friday.
Three investigators from the French air accident investigation bureau, along with a technical adviser from Airbus, have joined the Egyptian inquiry.
The BBC has learned the plane that disappeared was forced to make an emergency landing in 2013 after the pilot noticed the engine overheating, but an official report said the defect had been repaired.
In October, an Airbus A321 operated by Russia's Metrojet blew up over Egypt's Sinai Peninsula, with all 224 people on board killed.
Sinai Province, a local affiliate of the Islamic State jihadist group, said it had smuggled a bomb on board.
