The deal gives the Perth-based a much bigger share of the Inter City Railways Limited (ICRL) partnership than the 49% it has in the pair's Virgin Rail Group which currently operates the West Coast Mainline.
Stagecoach chairman and co-founder Sir Brian Souter said: "We have exciting plans for the franchise and, if selected, it would be our intention to operate Virgin-branded trains and maximise the potential of the brand to significantly grow passenger volumes on what is a key part of the UK rail network."
The East Coast shortlist will be announced in January and the contract awarded in October with the franchise starting in February 2015. The other bidders include FirstGroup.
Stagecoach yesterday complained of "frustrating" delays to deals to extend its West Coast and South Western franchises following problems with the system of franchise bidding last year. It now expects decisions in the second half of 2014.
Virgin Rail gets 1% of revenue in profit but wants to rework this for the extended deal to 2017 so it can earn higher profits but take more financial risk.
Stagecoach finance director Ross Paterson was dismissive of any attempt by a future Labour government to renationalise routes. He said the West Coast route had better punctuality than the state-run East Coast.
"If they (Labour) were in power I think (shadow chancellor) Ed Balls and the guys understand the economics of this. It could cost them a lot of money," he said.