Malaysia, Australia and China suspended a nearly three-year search in the southern Indian Ocean in January after scouring 120 000 square kilometers of remote seabed and failing to find any trace of Malaysia Airlines Flight 370.
Ocean Infinity said it remained hopeful that Malaysia would accept its offer to continue the search using a team of advanced, fast-moving deep-sea drones fitted with sonar equipment.
"The terms of the offer are confidential, but I can ... confirm that Ocean Infinity have offered to take on the economic risk of a renewed search," the company said in an email.
"We're in a constructive dialogue with the relevant authorities and are hopeful that the offer will be accepted," it added.
In Malaysia's hands
Voice370, a support group for families of the 239 people on board, said under the terms of the offer made in April, Ocean Infinity "would like to be paid a reward if and only if it finds the main debris field."
"Why hasn't Malaysia accepted this win-win offer?" Voice370 asked in a statement.
Malaysia did not immediately respond on Friday to the families' question.
An international 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 area of ocean on the northern boundary of the last search zone, far southwest of Australia.
But Malaysia, Australia and China agree that the newly identified area is too big to justify resuming the publicly funded search, which has already cost $160 million.
Australia has coordinated the search on Malaysia's behalf because Flight 370 crashed in Australia's zone of search and rescue responsibility on March 8, 2014, after flying far off course on a journey from Kuala Lumpur, Malaysia, to Beijing.
Transport Minister Darren Chester declined to comment on the possibility of a private search.
"Malaysia, as the state of registry for the aircraft, retains overall authority for any future search and any questions regarding possible future search efforts should be directed there," his office said in a statement.
"Australia stands ready to assist the Malaysian government in any way it can," it added.