No trace of the Boeing 777, which disappeared in March 2014 with 239 people on board, was found during a lengthy deep sea hunt in the southern Indian Ocean off western Australia, with the search called off in January.
Ocean Infinity, a seabed exploration firm which says it has the world's largest and most advanced commercial fleet of underwater vehicles for conducting searches, said it had proposed continuing the hunt.
Malaysia's Deputy Transport Minister Aziz Kaprawi confirmed a company had made an approach and was only asking for payment in the event they find the plane.
He said the firm had made a "good offer", and added negotiations were ongoing with the country's Department of Civil Aviation.
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"The company is demanding payment in the event the wreckage is found," he told AFP. "We have to work out the details, what we want most is the wreckage and the black box."
Grace Nathan, a Malaysian lawyer whose mother Anne Daisy was on the plane, urged authorities to accept the offer.
"There is no point waiting any longer, we really do not lose anything," she said. "It seems to be a perfect offer from a company that is equipped to undertake this search."
So far, three fragments of MH370 have been found on western Indian Ocean shores, including a two-metre wing part known as a flaperon.
But the country's transport minister previously said the underwater probe would not resume unless new evidence about the specific location of the aircraft emerge.
Ocean Infinity has a fleet of six underwater vehicles which can collect seabed data at a depth of 6,000 metres.
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