The navy vessel caught fire and sank on October 6 after running aground on a coral reef off the coast of Upolu.
The barge, which left New Zealand in November, is now near the vessel, after being reconfigured in Apia to handle diving operations.
The Samoan government gave the green light to the salvors to start the work needed to secure the barge over the ship.
The deputy chief of the navy Commodore Andrew Brown told RNZ Pacific that six anchors were in position.
"Weather permitting, the salvor will continue laying underwater installations which will connect the surface mooring lines to the barge. Once the barge is safely over the Manawanui and safely securely in place, the salvor will begin fuel extraction."
An interim report into the disaster has determined the cause of the grounding was human error.
