Kuala Lumpur: Malaysia and Australia will sign a deal specifying who handles any wreckage from missing flight MH370 that may be recovered, including the crucial "black box" flight data recorders, local media reports.

Malaysia is drafting the agreement "to safeguard both nations from any legal pitfalls that may surface during that (recovery) phase," the New Straits Times reported on Friday.

The government hopes the deal can be finalised soon and endorsed in a cabinet meeting next week.

The Australian government is studying the memorandum of understanding (MoU), it said.