Poor sea conditions on Saturday morning led the salvage team to temporarily abandon the operation.
It had been hoped to move the 17,000-tonne structure, which ran aground in August, to the transport ship the Hawk.
Now officials have confirmed the rig could be towed away from Broad Bay where it has been awaiting transfer.
Hugh Shaw, the UK government's official overseeing the operation, said: "Broad Bay is still the preferred point at the moment, so we will maintain the Hawk in that position and the rig on anchor.
"But we are looking further afield to see if there are any other lochs or areas in close proximity to here, either on the island itself or towards the mainland, where we may be able to tuck the rig and the Hawk in and get a little bit more shelter from the swell."
The Transocean Winner will eventually be transported to Turkey where it will be scrapped.
The oil drilling rig Transocean Winner may be moved to calmer seas after attempts to load it on to a transport ship off Lewis had to be postponed.