"We're at the final lap within these two weeks," the minister, Liow Tiong Lai told reporters. "We hope we can find the plane."
Liow did not specify a date but said that a tripartite meeting will be held after a final report is released when the 120,000 square kilometre search ends.
Authorities had previously said the search will end early this year. The last search vessel embarked on its final sweep across the southern Indian Ocean last month.
It is believed that the Malaysian Airlines plane crashed into the Indian Ocean, but an extensive deep-sea hunt off Australia's west coast has failed to find a single piece of debris.
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The Australian Transport Safety Bureau (ATSB), which has been leading the search mission, said in a report last month that the Boeing jet is almost certainly not in the current search zone and may be further north.
The report was based on a review of evidence by Australian and international experts.
The governments of Australia, Malaysia and China, where most of the passengers were from, previously agreed to pull the plug on the operation once the current search area was fully scoured unless "credible new information" emerged.
"We cannot just base [a search] on assumptions. We need credible clues to look for the plane," said Liow when asked about the possibility of a search further north.
Many families have been long sceptical about whether the ongoing search is in the right place.
In a statement late Thursday, the international group of MH370 next-of-kin, Voice 370, called on Malaysia, Australia and China to consider the next step before the current search ends.