Serco is understood to have pledged new coaches and top-notch catering for the sleepers, which ministers want significantly improved to make them “emblematic of Scotland”.
One source said: “The chat is their bid is superb.”
An announcement is expected to be made by next week.
The Scottish Government said yesterday that it was still negotiating with more than one of the three short-listed bidders for the 15-year contract starting next year.
An industry source said: “I hear stuff about new rolling stock, several different ‘classes’ and that they’ve gone to town with the hospitality thing.”
A separate source said: “I have heard Serco appears to be in the lead. I think the rumour is pretty solid.”
Serco runs Great Southern Rail in Australia, which operates four coast-to-coast routes such as The Ghan between Adelaide and Darwin, and the Indian Pacific from Perth to Sydney.
The trains have three classes, including platinum service, which offers “a heightened level of comfort to elevate your onboard experience to a truly global standard of luxurious travel”.
Ministers have encouraged bidders to include en-suite cabins and “premium” dining in their plans as part of a radical overhaul of the sleeper, backed by £110 million from the Scottish and UK governments.
The upgrade, which is expected to take up to three years, would also “showcase the best of Scottish cuisine”.
The trains run between Euston and Edinburgh, Glasgow, Aberdeen, Fort William and Inverness, carrying 270,000 passengers per year.
If the speculation proves correct, it would be a major blow to FirstGroup, which has run the service for ten years as part of the ScotRail franchise.
The Aberdeen-based firm is also bidding to retain control of the rest of ScotRail – the Scottish Government’s biggest contract at some £2.5 billion – as part of a new, separate franchise.
Industry experts warned that awarding the sleeper franchise to Serco could be a difficult political “sell”.
They pointed to the scandal over the company, which manages wide-ranging government contracts, overcharging UK ministers for tagging criminals.
Serco’s operation of Northlink ferries to Orkney and Shetland has also been criticised over staff cuts and service reliability.
The third sleeper bidder is Arriva, owned by Germanoperator Deutsche Bahn.
One source said: “Lots of chat about Serco winning, but there are reputation issues after troubles south of the Border over prisons, plus Northlink up here.”
It is understood the speculation over Serco being in pole position relates to signs the company has been holding more negotiations with the Scottish Government’s Transport Scotland agency than the others.
Another source said: “A pretty heavy, big team of Serco corporate people were seen arriving in Glasgow a few weeks ago. We got a distinct impression they were there to negotiate.”
Professor Jim Gallacher, a former board member of watchdog body Passenger Focus, said Caledonian Sleeper was currently inferior to the best elsewhere, with patchy catering.
He said of the Paris-Madrid sleeper: “It is a very high-quality experience, with en suite facilities and a very good dining car.”
A Scottish Government spokesman said: “Section 2.18 of the invitation to tender says that following the bid evaluation and clarification, Transport Scotland reserves the right to negotiate with one, some, or all bidders.
“This is the stage that we are currently at, and we can confirm that we are engaged in legal negotiations with more than one bidder.”
All three bidders declined to comment.