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Local authorities in the state of Victoria, Australia, are working to plug fuel leaks in a stricken fishing trawler that has sunk in Port Phillip Bay.

The 27-metre Lady Cheryl ran aground near Point Nepean at 1.20am on Saturday.

Victorian Ports Minister Denis Napthine said the vessel was intact and had been anchored at three points to keep it from shifting.

"It is hoped the divers can cap and seal those leaks and then the vessel can be salvaged with the fuel tank largely intact," Napthine told reporters.

Napthine said that while it was unknown exactly how much of the 30,000 litres of diesel in the vessel's tank had leaked, it was 'only small amount'. The trawler was also carrying several hundred litres of hydraulic fluid and commercial lubricant.

A plume of diesel was seen to be leaking into surrounding waters off Point Nepean National Park over the weekend. State marine pollution controller Donovan Croucamp confirmed that the vessel had been leaking a 'relatively small amount of fuel'.

The Port of Melbourne Corporation is coordinating the salvage operation. Denis Napthine was unable to confirm how long it would be before the trawler could be moved.

"It's not going to sit there forever; it's going to be salvaged in a timely manner," Napthine said.

The six crew onboard the Lady Cheryl were rescued. According to media reports, the 42-year old captain is alleged to have recorded a blood alcohol reading over the legal limit and could be charged by police.

Commenting on the issue, Opposition Leader Daniel Andrews told AAP: "Just as it is irresponsible and dangerous to get behind the wheel of a car if you're over the blood alcohol limit, equally vessels at sea need to be in control of people who have all their faculties."