The Joint Agency Coordination Centre (JACC) managing the multinational search for the missing plane said it continued to believe that the plane came down in the southern Indian Ocean off Australia.
The Bay of Bengal is located between India and Myanmar, thousands of miles from the current search area. The wreckage was reported by Australian geophysical survey company GeoResonance.
"The company is not declaring this is MH370, however it should be investigated," GeoResonance said in a statement.
The company said it had passed on the information to Malaysian Airlines and the Malaysian and Chinese embassies in Australia on March 31, and to the JACC on April 4.
"The company and its directors are surprised by the lack of response from the various authorities," GeoResonance said.
"This may be due to a lack of understanding of the company's technological capabilities, or the JACC is extremely busy, or the belief that the current search in the Southern Indian Ocean is the only plausible location of the wreckage."
GeoResonance says on its website that it offers a unique and proven method of geophysical survey that detects electromagnetic fields from various chemical elements. GeoResonance did not respond to requests for further comment.
Flight MH370, carrying 227 passengers and 12 crew, went missing in March en route from Kuala Lumpur to Beijing.
The Australian-led search team said it was relying on information from satellite and other data to determine the missing aircraft's location and the location in the GeoResonance report was not within that search arc.
"The joint international team is satisfied that the final resting place of the missing aircraft is in the southerly portion of the search arc," it said.
A massive search operation involving aircraft, ships and sophisticated underwater equipment capable of scouring the ocean floor has so far failed to turn up any trace of the plane.
Australia's Prime Minister Tony Abbott said on Monday the chance of finding floating debris was now remote, and a new phase of the search would focus on the seabed.
Malaysia's transport ministry said in a statement late on Tuesday that it was assessing the credibility of the latest report.
"In line with Malaysia's consistent stand of verifying and corroborating any new lead since Day 1 of the search operations, we are aware of a report citing the detection of potential aircraft wreckage in the Bay of Bengal," said Acting Transport Minister Hishammuddin Hussein.
"Malaysia is working with its international partners to assess the credibility of this information."