The drilling rig came ashore at Dalmore, near Carloway on Lewis, during a storm almost two weeks ago. It was being towed from Norway to Malta.
Those involved in the operation to salvage the rig suggested the structure might be refloated over the weekend.
However, they stressed that this would only happen if it was deemed safe to do so.
Over the past few days equipment to improve the buoyancy and stability of Transocean Winner has been brought on board the structure.
More than 12,000 gallons (56,000 litres) of diesel oil were lost from two tanks on the Transocean Winner after it came ashore. The fuel is said to have evaporated and not caused a pollution incident.
Tens of thousands of gallons of the fuel remain in other tanks on the decommissioned rig.
Once refloated Transocean Winner would be towed to a nearby location at sea for further checks for damage.
Preparations for the refloat of the 17,000-tonne grounded rig Transocean Winner have been continuing.