Bermuda-registered Sea Containers is said to be ready to ditch the east coast main line operator in a bid to raise £200m and stave off bankruptcy in the US.
GNER has been running services between London, Leeds and Scotland since 1996, and recently won a new 10-year franchise for the route.
Two of the competitors which GNER beat in the franchise race, FirstGroup and Virgin Trains, were today being tipped as likely bidders if the York-based business did end up on the market.
Sea Containers, listed on the New York Stock Exchange, is reported to need extra funds to settle debts after breaching lending agreements with its bankers.
Last month GNER dropped out of the running for the UK's new South Western rail franchise, saying resources were required elsewhere.
It is also waiting for the outcome of a judicial review into the Office of Rail Regulation's decision to allow its rival firm Grand Central to operate thenew London to Sunderland services on the east coast main line.