Neither Ocean Infinity nor the Malaysian government have said when the proposal was made.
The exploration company, Houston-based Ocean Infinity, offered to undertake the project and "the economic risk" for a fee only if it finds the wreckage of the plane, CNN reported Friday.
Australia's national science body CSIRO said in April that MH370 was "most likely" lying north of the former search zone - a 120,000 square kilometre (46,000 square mile) area largely defined through satellite "pings" and the flight's estimated fuel load.
Malaysian authorities have said discussions are ongoing and the firm only wants payment if the aircraft is found.Voice 370, an worldwide group of MH370 next-of-kin, urged authorities to take up the offer, saying in a statement: "Why hasn't Malaysia accepted this win - win offer?"
"Why hasn't Malaysia accepted this win-win offer?" "We're in a constructive dialogue with the relevant authorities and are hopeful that the offer will be accepted". Voice370 asked in a statement.
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Malaysia, Australia and China which began the search sending their respective teams had announced in January this year that they were suspending the search for MH370, which vanished while flying from Kuala Lumpur to Beijing on March 8, 2014.
An worldwide board of experts has concluded, based on analysis of Boeing 777 debris that drifted and washed up on western Indian Ocean beaches, the flight most likely crashed in a 25,000-square-kilometer (9,700-square-mile) area of ocean on the northern boundary of the last search zone, far southwest of Australia.
Speaking to NBC News, Darren Chester, Australia's transport minister, stated that since the aircraft was registered in Malaysia, that country "retains overall authority for any future search [efforts]". China, where most of the passengers came from, and Australia were both involved in the search.
"Australia stands ready to assist the Malaysian government in any way it can", it added.