The damaged twin-engine Cessna was found near what looks to be a make-shift runway on Monday near Papa Lealea about 30km north-west of Port Moresby, the Australian Broadcasting Corporation reported.
Authorities were alerted to the plane's presence the previous day when its emergency locator transmitter was activated.
The Accident Investigation Commission has confirmed the plane was involved in an accident but it's too early to say what happened.
Flight tracking websites show the plane left the Mareeba airport in Far North Queensland on Sunday morning, heading north.
A source close to the investigation said the plane was not cleared to enter PNG.
PNG police deputy commissioner Donald Yamasombi told local media his officers are looking for the Australian pilot but did not reveal his identity.
Port Moresby-based Australian Federal Police are assisting with the investigation.
A search of Australia's Civil Aviation Safety Authority's register shows the Cessna's registration holder is a PNG company called Ravenpol No. 69.
Company documents show its sole director and shareholder is Geoffrey Paul Bull, but several sources have said he was murdered in Port Moresby last year.
According to the aircraft register Ravenpol became the registration holder in January this year, after Bull's death.
CASA's register also show the plane's registered operator is Alice Springs-based aviation company Avlease.
But Avlease director Ian Scheyer said his company had never operated the Cessna and he could not explain why his company is listed on CASA's registry.
"I can put my hand on my heart and say we've never operated it," he said.