MELBOURNE, Nov 14 (Reuters) - AGL Energy (AGL.AX) is considering importing liquefied natural gas (LNG) to southeastern Australia from 2021, in a move that could ease the grip on supply that four producers led by ExxonMobil Corp (XOM.N) hold in the region.

Australia is on track to become the world's top exporter of LNG, but that is paradoxically creating a shortage at home as gas is pulled away from local markets in the southeast.

AGL on Monday said it was running a A$17 million ($13 million) study on building an LNG import terminal and aimed to make a final investment decision in 2018-19 on a project that it estimated would cost between A$200 million and A$300 million.

It has identified a number of sites and a terminal could be available by 2021, according to slides prepared for its investor day on Monday.

A map highlighted imports could come from as far away as Europe, the Middle East, Africa, the United States and Asia, despite the fact that by then Australia will have 10 plants exporting LNG.

"We are really staring through the looking glass when the world's largest exporter of LNG is considering importing gas in the face of unaffordable domestic prices," said Bruce Robertson, an analyst at the Institute for Energy Economics and Financial Analysis.

In a taste of what would happen without new sources of gas, prices in Victoria rocketed in July to six times the level of Asian LNG during a cold snap, as demand had to be met with gas diverted from LNG plants in Queensland and piped roughly 2,000 kilometres south.

The gas price spike highlighted concerns raised earlier this year by Australia's competition regulator about the grip that ExxonMobil, BHP Billiton (BHP.AX) (BLT.L) , Origin Energy (ORG.AX) and Santos (STO.AX) have on domestic gas supply.

The watchdog also flagged that hefty charges on unregulated pipelines were limiting movements of gas and warned that state bans on onshore gas drilling were also curbing new supply.

The Australian Energy Market Operator sees a shortfall in domestic gas looming after 2019.

($1 = 1.3256 Australian dollars)