Hugh Shaw, the UK government official overseeing the salvage operation, said preparations were being made to allow the Hawk to begin the journey to Malta.
From Malta the 17,000-tonne drilling rig is to be taken to a yard in Turkey to be broken up.
The structure ran aground at Dalmore on Lewis in a storm in early August while being towed to Malta.
Last week, Transocean Winner was floated on to the deck of the Hawk, a semi-submersible ship used for transporting large maritime structures over long distances.

Long before Donald Trump had his eye on the White House, his attention was firmly on the small community of Menie in Aberdeenshire. The American businessman wanted to build the greatest golf course on earth.
However, some people who lived in the area became vehemently opposed, and the saga of the Trump International Golf Links began.
"I saw that the residents of Menie were getting a lot of bad press at a time when Donald Trump was being celebrated for arriving in the area," reflected Alicia Bruce, a photographer who spent six years capturing the changing landscape of Menie and its people as the course was built on rare sand dunes.
Alicia was speaking from the Luvians Ice Cream parlour and cafÃ© in St Andrews, a novel choice to host her photography project. Festival organisers are keen to bring the exhibits out of the gallery and into the community.
It was indeed a sense of community that first drew Alicia to the project. She grew up in Aberdeen, and played on the beaches in Menie in her childhood.
As Donald Trump told the assembled media of his intentions to transform the area into a haven for golf fans around the world, Alicia wanted to discover the story of the locals who lived there.  She has never photographed the businessman, focussing instead on the residents and the changes to the environment.
The pictures of the Menie locals are based on portrait paintings they chose themselves.
She said: "I started off by going to visit Michael Forbes and instead of finding the angry peasant, pig, village idiot that Donald Trump called him, I found this hospitable, lovely guy surrounded by friends and family."
Mr Forbes became the face of the community who stood up to the billionaire property developer. He was one of the main contributors in Anthony Baxter's award winning documentary You've Been Trumped.
Alicia's image of Mr Forbes, which is also on display in the Scottish National Portrait Gallery in Edinburgh, is one of the key pictures of her collection.
During one of her visits to Menie however, she became the subject of some unwanted attention.
"I was threatened by Donald Trump's security," she adds.
"It was quite frightening. I was there to visit [Menie Resident] Susan Munro as a friend that day and I had my camera with me.
"I just wanted to take a picture of where the clubhouse was going to be. I was on her land.
"Out of nowhere, this security guard comes along and starts threatening me and says he is going to 'smash my camera'. He was really angry."
In relation to that incident, which happened in June 2012, Grampian Police issued a formal police warning to the individual over threatening and abusive behaviour.
When asked about the allegations of bullying that have been made against the Trump organisation in relation to the Menie golf course development, Sarah Malone - the Executive Vice President of Trump International Golf Links - stated they are "categorically untrue".
Ms Malone also pointed out the golf course's success since it opened four years ago, attracting tens of thousands of visitors, adding the venue is "hailed by industry chiefs and the greatest names in golf as a modern masterpiece and a must play for every golfer".
With 150 people currently employed on the course, Ms Malone also highlighted plans for the development to expand including a second golf course, hotel and luxury villas.
For Alicia, she is making final preparations for a talk she will give on Wednesday, 7 September, at the festival about her experiences at Menie.
"I think it is unfortunate that an area of outstanding natural beauty has been short-sightedly changed for leisure," she concludes.
"The residents themselves and plenty environmental experts advised there were other ways to design the golf course which wouldn't have had such an impact."
The rig Transocean Winner is expected to be moved on a heavy lift ship from Broad Bay, Lewis, on Wednesday.
[NEXT_CONCEPT]
The story of the American Presidential hopeful and the Aberdeenshire locals who stood up to him is now being told in St Andrews, the home of golf, at the town's inaugural photography festival.