The airline said in a statement it was looking at the possibility that the plane tried to return to an airport at Subang, near the capital, Kuala Lumpur.
But the statement stressed officials were looking at all possibilities.
Beijing-bound flight MH370 vanished on Saturday shortly after it left Kuala Lumpur. There were 239 people on board.
In a statement, Malaysia Airlines said: “The search and rescue teams have expanded the scope beyond the flight path. The focus now is on the West Peninsular of Malaysia at the Straits of Malacca.
“The authorities are looking at a possibility of an attempt made by MH370 to turn back to Subang… Apart from the search in the sea, search on land in between these areas is also conducted.”
Rescue teams from several countries are scouring the seas for signs of the plane.
Malaysian authorities said on Monday they were expanding the search area from 50 nautical miles from where the plane had disappeared – over waters between Malaysia and Vietnam – to 100 nautical miles (115 miles; 185km).
Relatives of the missing passengers – most of whom were Chinese – have been told to prepare for the worst.
China’s Xi’an Satellite Control Centre launched an emergency response and adjusted the operations of up to 10 orbiting satellites to help in the search, a website run by the People’s Liberation Army said late on Monday.
Meanwhile, Boeing said that it had joined the US National Transportation Safety Board team as a technical advisor. The team has positioned a group of investigators and technical advisers in Asia to offer assistance.
At least 40 ships and 34 aircraft are taking part in the search in the seas off Vietnam and Malaysia.
Search and rescue teams from Australia, China, Thailand, Indonesia, Singapore, Vietnam, Philippines, New Zealand and the United States of America are assisting, Malaysia Airlines said.
On Monday, people gathered in Malaysian capital Kuala Lumpur to hold a candlelight vigil for the missing passengers.
Families in Beijing and Kuala Lumpur have expressed frustration at the lack of information about the plane’s fate.
Flight MH370 left Kuala Lumpur for Beijing at 00:41 local time on Saturday (16:41 GMT on Friday). But radio contact was lost at 17:30 GMT, somewhere between Malaysia and Vietnam.
Officials say they still have no idea what went wrong.
None of the debris and oil slicks spotted in the water so far have proven to be linked to the disappearance.
Authorities are also investigating two men who boarded the missing plane on Italian and Austrian passports stolen in Thailand years ago.
Malaysian police said they had identified one of the men. They did not reveal his identity, but confirmed the man was not Malaysian.
Experts say the presence of two passengers with stolen passports is a breach of security, but is relatively common in the region and could relate to illegal migration.
The passengers on the flight were of 14 different nationalities. Two-thirds were from China, while others were from elsewhere in Asia, North America and Europe.
Malaysia Airlines is the country’s national carrier, flying nearly 37,000 passengers daily to some 80 destinations worldwide.