(Adds talks details, families' comments; paragraphs 6-11, 13-16)
KUALA LUMPUR, Oct 19 (Reuters) - Malaysia is negotiating with U.S.-based seabed exploration firm Ocean Infinity to resume the search for Malaysia Airlines MH370, which vanished three years ago in the southern Indian Ocean with 239 people aboard.
The disappearance of the aircraft en route to Beijing from Kuala Lumpur ranks among the world's greatest aviation mysteries after Australia, China and Malaysia ended a fruitless A$200-million ($157-million) search effort in January.
This week, Malaysia said it had received proposals to continue the search from Ocean Infinity, Dutch firm Fugro and an unidentified Malaysian company. Infinity beat out the competition and the government has begun negotiations with it, Malaysia's deputy transport minister Aziz Kaprawi said on Thursday.
"Yes, we are negotiating with Ocean Infinity, but the agreement has not been finalised," he told Reuters, but declined to comment on the potential reward for the plane's discovery.
"It was an offer on an open basis, that we will only honour if the aircraft is found."
The firm had made an offer on a "no-cure, no-fee" basis, according to a letter, seen by Reuters, that was sent to passengers' families on Thursday.
Australia and China were informed of the negotiation process, but only Australia had informally agreed to Malaysia's choice, Aziz said.
"It is still under discussion with China," he added, but declined to elaborate on China's possible concerns.
Australian and Chinese authorities did not immediately respond to Reuters' requests for comment.
Ocean Infinity could not confirm the award of a contract, "but good progress has been made", a spokesman said in a statement.
Calvin Shim, whose wife was one of the MH370 crew, said he was relieved authorities were considering resuming the search.
"Grateful this step is finally being officially taken," he told Reuters in a text message.
Relatives of others on board voiced concern over the lengthy talks, however. Families were told of Ocean Infinity's offer in March, said Grace Nathan, a lawyer whose mother was aboard.
"The best weather for the search is spring and summer," said Nathan. "We worry they will lose that window if they take too long to decide."