Sir Richard Branson has offered to run the West Coast Mainline "for free" to give Parliament time to review the £10bn franchise's award to FirstGroup.He said Virgin Trains and Stagecoach would run it on a not-for-profit basis after December - when they are due to hand over the franchise - if more time was needed for a review.
More than 100,000 people have signed an online petition against the decision.
FirstGroup said it would bring in key improvements for passengers.
In its bid, FirstGroup said it would introduce better wi-fi and food, more frequent trains and more seats, and would cut standard fares by 15%.
The firm said it would introduce 11 new 125mph six-car electric trains on the Birmingham-to-Glasgow route and provide more direct services between destinations.
'Almost certain bankruptcy' However, the Virgin boss claimed promises made by FirstGroup in its successful bid were unrealistic and would lead to his rival's "almost certain bankruptcy".
In an opinion piece in the Daily Telegraph, Sir Richard described the government's decision as "outrageous, unjust and simply wrong".
His campaign to have the decision reviewed has been backed by businessman Lord Sugar, TV chef Jamie Oliver and the double Olympic gold medallist Mo Farah.
The government is due to sign the 13-year contract with FirstGroup on Tuesday, following the Department for Transport's decision earlier this month.
Louise Ellman, who chairs the House of Commons transport committee, has written to Transport Secretary Justine Greening asking her to delay signing the contract.
But a Department for Transport (DfT) spokesman said: "We note the offer that one of the bidders appears to have made via the press.
"However, the winning bidder was decided by a fair and established process and no reason has been advanced to convince DfT not to sign the agreement."
Virgin has run the franchise since 1997, during which time passenger numbers have doubled, but has been told that its tenure will end on 9 December.
Sir Richard said that if reviewing the decision meant the December deadline had to be postponed, his company and Stagecoach would be willing to continue operating the railway lines while donating any profits to charity.
The government says FirstGroup's new trains should add a further 12,000 seats a day on West Coast routes from 2016.
FirstGroup said it already ran an award-winning service and was looking forward to welcoming new passengers.
"As a result of our plans, customers travelling with us will use faster brand new trains with more seats, serving more destinations than the current service," a spokesman said.
"There will be improved wi-fi, better catering, refurbished stations and importantly we'll be cutting standard anytime fares by 15% on average."
About 31 million passengers travel on the West Coast Mainline every year.