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.