The stricken cruise liner The Norwegian Star is expected to arrive in Port Melbourne this afternoon.
Melbourne's Herald Sun has reported Norwegian Cruise Lines representative Rhea Dsouza saying this morning that tugboats had reached the vessel and were pulling it in.
Thousands of distressed passengers are onboard the cruise ship bound for New Zealand that broke down in the Tasman Sea about 50km from Melbourne with more than 2000 people aboard.
A passenger onboard the ship told The Age some people were crying.
"We're stuck in the middle of the ocean. It's scary," the man told The Age.
Steve T Raney posted on Facebook saying: "WE have NO engines for propulsion!!! WE are afloat in the ocean!!!"
Raney said on Facebook that passengers were safe and comfortable and tugboats were on their way to tow the Norwegian Star back to Melbourne.
"We are returning to Melbourne for 4-5 days as soon as they can get boats out here to us to pull us in. This just announced by the ship's captain," he said.
A spokeswoman for operator Norwegian Cruise Lines said the ship's azipod propulsion system experienced a technical malfunction in the early hours of this morning.
"The ship has full power and all onboard services are fully operational. All guest amenities remain open and available.
Meanwhile, cruise ship the Emerald Princess has departed Port Chalmers following a fatal accident that claimed the life a crew member earlier this week.
The Filipino man was killed by an exploding gas cylinder. The ship was delayed while investigators probed the death but the ship departed the port yesterday.