Flight MH370 disappeared in March 2014, en route from Kuala Lumpur to Beijing, with 239 passengers and crew on board. Ocean Infinity was taking advantage of favorable weather to move the vessel toward "the vicinity of the possible search zone", the company said in a statement.
No sign of the plane was found in a 120,000 square kilometre search zone selected by satellite analysis of the jet's likely trajectory.
Malaysia's Deputy Transport Minister Aziz Kaprawi said negotiations for the firm to restart the hunt on a "no find, no fee" basis were in the final stages.
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Liow added the contract would be finalized by next week.
The message, seen by AFP, said that the "MH370 Response Team wishes to note that the Government of Malaysia has engaged Ocean Infinity to undertake further search operation for MH370".
Through a text sent to the victims'families, the company, which specializes in the exploration of the seabed, explained that a reconnaissance vessel has already entered the search area this week.
But a report from the Australian Transport Safety Board released later in the year pointed to a new area where the plane could be found.
Sub-equipped ship departs South Africa to search for MH370 The search vessel named Seabed Constructor left the South African port of Durban on Tuesday as part of the Ocean Infinity company's plan to look for debris in the southern Indian Ocean.