Virgin Rail has offered to pay more than $9.3 billion for the franchise to operate the West Coast main line -- a route running from London to Glasgow that Branson's company has run with its partner Stagecoach for the past 15 years, The Daily Telegraph reported Saturday.
However, rival FirstGroup has offered nearly $11 billion for the 14-year West Coast contract starting in December.
The British government has not yet announced a winner of the contract.
In an effort to bolster his chances of obtaining the contract, Branson sent a letter to Transport Secretary Justine Greening, and copied to David Cameron, calling FirstGroup's proposal "unrealistic," claiming the only way FirstGroup can justify its bid is to "drastically cut the quality of services" along the line over the life of the contract.
A senior official at a rival transport group seemed to agree with Branson.
"Virgin Rail's bid is already aggressive. Yet FirstGroup is said to be bidding 1 billion pounds [$1.56 million] more. We think that requires 8.5 percent to 9 percent growth every year for 14 years off the back of a double-dip recession. That just beggars belief."
In his letter, Branson also noted his company's takeover of the East Coast main line after two other companies, GNER and National Express, walked out on their contracts for that line in 2005 and 2007 respectively.
Branson said Virgin Rail made "realistic bids after an extremely expensive tendering process" only to be beaten by both rivals that came "nowhere close to delivering their promised plan."
Neither FirstGroup nor the government have commented on the current situation.