The temporary fix has been proposed by the Department for Transport after its embarrassing U-turn over the award of a new franchise earlier this month.
Virgin's current franchise is due to end on December 9 but talks are under way about it remaining as operator for between nine and 13 months while a competition is run for an interim franchise agreement.
Three Department for Transport (DfT) civil servants were suspended after the West Coast bidding competition was halted on October 3 when "significant technical flaws" were found in the way the franchise process had been conducted.
Virgin has run the West Coast line since 1997 but in August the DfT announced that a new 13-year franchise for the London to Scotland line had been awarded not to Virgin but to rival transport company FirstGroup.
Virgin boss Sir Richard Branson launched a legal challenge to the decision, describing the bidding process as "insane".
It was while getting itself ready to fight the legal challenge that the DfT discovered the flaws in the bidding.
The DfT's original decision was made when Justine Greening was Transport Secretary.
Both she and her successor, Patrick McLoughlin, had defended the bidding process in the light of Sir Richard's comments and legal challenge, with Mr McLoughlin telling a Commons Select Committee he was happy with the way the bidding had been conducted.
Mr McLoughlin said today: "The cancellation of the InterCity West Coast franchise is deeply regrettable and I apologise to the bidders involved and taxpayers who have a right to expect better.
"My priority now is to fix the problem and the first step is to take urgent action to ensure that on December 9 services continue to run to the same standard and passengers are not affected.
"I believe Virgin remaining as operator for a short period of time is the best way to do this and my officials and I will be working flat out to make this happen."
The DfT has also paused the ongoing franchise programme including live competitions on Essex Thameside, Great Western and Thameslink and set up two independent reviews into what went wrong with the West Coast competition and the wider DfT rail franchise programme.
The RMT transport union had been hoping that Mr McLoughlin would announce that the West Coast franchise would be run by the DfT in the public sector as is the case, at the moment, with the East Coast franchise.
Today RMT leader Bob Crow said: "This announcement is no surprise. The Government are ideologically opposed to public ownership of the railways and, in collusion with the private train operators, have stitched up a shabby deal that will enable them to rerun the whole franchise fiasco in a year's time.
"Richard Branson and his shareholders are laughing all the way to the bank. Not only have they made hundreds of millions from the rail privatisation lottery but they have now scooped the rollover as well.
"We will continue to fight for public ownership of the railways, a position supported by the vast majority of the British people. This short-term political fix will not detract from the call for rail to be run as a public service free from the chaos and greed of privatisation."
Manuel Cortes, leader of the TSSA rail union, said: "This decision means that the long-running Whitehall farce, known as private rail franchising, continues at the taxpayer's expense.
"We, the public, continue to subsidise a billionaire to run a railway line which would cost less if it was in the public sector. Our Alice-in-Wonderland railway system is beyond the dreams of fiction."
Virgin has more than doubled annual passenger numbers on West Coast, introducing the now familiar high-speed tilting Pendolino trains.
When he heard that Virgin had lost the franchise this summer, Sir Richard questioned FirstGroup's ability to fulfil its franchise promises.
He also highlighted the problems with East Coast where first GNER and then National Express had to give up their franchises, with the East Coast now having been run by the DfT since November 2009.
A Virgin Trains spokesman said: "Our customers have made clear they want us to continue our excellent service and we now have the chance to deliver that and offer customers some short-term continuity.
"We will now be working hard to make sure we continue to provide the service that has made us successful. We are grateful for the fantastic support from customers and staff over recent months."
FirstGroup said today: "We believe the private sector provides the most effective and efficient way to deliver passenger rail services in the UK.
"We await the outcome of the independent investigations into the West Coast franchise competition and the wider rail franchising process, which we hope will provide a greater degree of certainty and confidence not only to future bidders but to employees, stakeholders and the travelling public too."