Under-siege National Express is facing more bid interest amid speculation that Stagecoach will join the race for the bus and rail group.

The Scottish-based group, whose franchises include South West Trains, was said to be considering whether to trump the £600 million offer expected from Spain’s Cosmen family and private equity’s CVC.

According to The Sunday Times, Stagecoach has appointed Deutsche Bank to draw up plans for an all-share takeover offer for Birmingham-based National Express. The tie-up would create a group with a significant share of UK transport markets and a strong presence in America.

The bid interest in National Express - which is set to lose its loss-making East Coast rail deal after failing to renegotiate the franchise - began earlier this month with interest from FirstGroup.

The UK’s biggest transport group walked away last week, just as it emerged that the biggest shareholder in National Express - the Cosmen family - had joined forces with CVC to table a proposal. A formal offer could come this week.

National Express shares surged strongly late last week ending Friday’s session 6.7 per cent up at 345.75p, valuing the business at £529,06 million.

Sunday's report said Deutsche Bank has been working on a Stagecoach bid for some weeks, well before the Cosmen interest became public.

If it does not make an offer for the entire company, Stagecoach may yet benefit as the Cosmens and CVC might not be interested in retaining National Express’s UK rail franchises and could attempt to hand them on.

Cash-strapped National Express, which is due to announce half-year figures on Thursday, had been contracted to run the East Coast franchise until 2015, but saw passenger growth stall in the recession.

The deal lost £20 million in the first half of this year.

As a result of handing over the East Coast franchise, it has been warned it could lose its two other rail franchises - East Anglia and commuter service c2c.

It also emerged that Sir Richard Branson’s Virgin Trains - a joint venture with Stagecoach - was mulling over a bid for the East Coast franchise.

Sir Richard told The Sunday Telegraph that he would bid for the line when it comes up for tender, expected to be late next year, if the Government makes changes to the franchise system.

Virgin lost out on two previous occasions for the East Coast line, most recently in 2007 when National Express bid £1.4 billion to win the franchise until 2015.

Sir Richard wants future bidding processes to take into account previous rail performance, future investment programmes and for the franchise period to be longer to spread the risk.

National Express is the West Midlands’ biggest bus company, operating nearly 550 routes across Birmingham, Coventry and the Black Country, and also runs the Midland Metro tram service linking the city centres of Birmingham and Wolverhampton. It is also the country’s biggest operator of long distance coaches.

The company was recently forced to give assurances that the promised new Digbeth Coach Station in Birmingham would open as planned in November after contractor Ashford Construction got into difficulties.