The Government is set to sign off on a controversial deal that will see the running of the West Coast Main Line removed from Virgin Trains.
Transport Secretary Justine Greening said that, despite the Commons Transport Select Committee wanting to examine the new deal, winning bidder FirstGroup and the Government would put pen to paper soon.
And she claimed that if Virgin had won the bid it would have "been perfectly happy with the process".
The 13-year deal is expected to be signed on Wednesday. A row has raged over Virgin losing its franchise and boss Sir Richard Branson offered to run the route free of charge to allow the decision to be re-examined.
The Labour Party also urged Mrs Greening not to sign off the contract until MPs have been able to scrutinise it in detail. More than 100,000 members of the public also signed an online petition against the decision, in a campaign supported by double Olympic champion Mo Farah, Apprentice star Lord Sugar and celebrity chef Jamie Oliver.
Mrs Greening told BBC Breakfast today that all bidders had "bought into" the "fair and well-established process".
She said: "We do plan to push on with signing the contract with FirstGroup and I do suspect that, although I have a huge amount of respect for Virgin and the work they have done on the line, I suspect that, had they won the bid, they would have been perfectly happy with the process."
On Sunday, Sir Richard urged the Prime Minister to "intervene to try to get some sense into the Department for Transport". He said with Mr Cameron and the Chancellor George Osborne away on holiday, a decision on signing the deal should be delayed by a month.
FirstGroup claims it will deliver better value for taxpayers. It plans major improvements to the InterCity West Coast franchise including improved wifi and catering, as well as additional services, more seats and reducing standard anytime fares by 15% on average.
Chief executive Tim O'Toole said: "We are pleased that the DfT has reiterated that our winning bid was selected by a fair, rigorous process that scrutinised best value and deliverability and that they concluded that no reason has been advanced to convince the DfT not to sign the agreement."