The Transocean Winner landed at Dalmore Bay on Lewis in August after detaching from its tug in stormy weather en route from Norway to Malta.
The rig, which was refloated during high tide after three weeks and anchored at the island’s Broad Bay, has now been disconnected from anchors and is being held on four tugs about half a mile from the semi-submersible heavy lift vessel OHT Hawk, which will take it to Turkey.
The Maritime and Coastguard Agency (MCA) said clear weather should allow the rig to be floated on to the Hawk on Friday.
Counter-pollution measures have been put in place and an MCA surveillance aircraft will scan the area from the air.
An MCA spokeswoman said: “Final preparations for moving the Transocean Winner rig onto the Hawk vessel are continuing and good progress has been made on the operation in Broad Bay.
“The anchors have now been disconnected and the rig is being held on four tugs about half a mile from the Hawk.
“The Hawk has almost completed ballasting and is making final preparations to receive the rig.
“Weather conditions are improving by the hour and if this continues, then it is extremely likely that the rig will be floated over the Hawk later this morning or early this afternoon.
“As long as the weather holds, the Transocean Winner will be loaded onto the Hawk and taken out of the water within the next 24 hours.
“The operation itself is, however, going to be lengthy.”
The rig’s grounding sparked pollution fears due to the 280 tonnes of diesel on board.
Investigations found two of its four fuel tanks were damaged in the incident which resulted in the loss of 53,000 litres of fuel, most of which is thought to have evaporated with no damage to the environment.
The remaining fuel has been safely removed.