The problem is reportedly serious enough to prompt the removal of the jet engine from beneath the plane's wing.
Mechanics have discovered leaking oil in three Qantas Airbus jet engines.
A Qantas official told the newspaper that oil was found where there should not be oil. The planes are relatively new, having been put into service in 2007.
According to a report in the Australian newspaper, The Age, the problem was found after Qantas grounded its fleet of six Airbus A380s, including three at LAX. The airplane in question is one of those three.
It was Thursday that an engine on an Airbus A380 exploded shortly after take-off and was forced to return to Singapore for an emergency landing.
"Leaks have been discovered in the turbine area of three engines," said Alan Joyce, Qantas' chief executive officer, at a news conference. "We have removed these engines from the aircraft for further testing. We are now planning that the A380 fleet will remain out of service for at least the next 72 hours."
Joyce said Qantas will replace the Rolls Royce engines of three of the affected aircraft, two of which are at LAX. The third is in Sydney.
Some 1,300 passengers worldwide have been stranded by the grounding of the fleet.
Qantas has deployed additional Boeing 747 jumbo aircraft to Sydney to fly out stranded passengers.
Traveler Bonnie Nystrom was able to keep her scheduled Qantas flight to Australia on Sunday night. She said she was impressed by how the airline has handled the situation.
"I was pleased that when I went online they had a place where you can look for disruptions, they had a lot of good information for people to find people who had been stranded," Nystrom said.