Trains on the main Edinburgh-Glasgow route could be diverted if required at Winchburgh in West Lothian onto a line via Dalmeny and the Fife line to rejoin the route at Saughton, west of Haymarket in Edinburgh.
The project, estimated by Network Rail to cost £150-250 million, would involve new junctions at Winchburgh and Dalmeny.
The work could effectively reinstate a part of the Edinburgh-Glasgow main line electrification project which was shelved in 2012 to save money.
Transport secretary Michael Matheson today announced £15m to develop the plans.
Three options for the new junctions will be explored.
Mr Matheson said the western approach to Edinburgh Waverley station was such a critical and busy part of the Scottish network that trains running even a few minutes late could cause significant delays to others and knock-on disruption across other routes.
He said: “With Edinburgh being a key economic driver for the country, a reliable train service is essential for commuter and business travel.
“It provides confidence to businesses and commuters alike that rail is the best option for their journey and thus enables the continued growth and prosperity of the city.
“One of the key aims of the Edinburgh Waverley Western Approaches project is to provide additional capacity to reduce these constraints, improve performance and give greater resilience across the railway.”
A Network Rail spokesperson said: “We are working closely with Transport Scotland to develop cost-effective proposals to expand the network to the west of Edinburgh - delivering increased flexibility and improved reliability for passengers and freight customers.”