It's been proposed to run direct train services from Reading to Heathrow. Network Rail is planning to build a £500m tunnel off the current Great Western line between the Berkshire town and Paddington by 2021 that will link into the airport.
The service will take less than 30 minutes and bring the airport within an hour of most towns in the south.
Heathrow Express say they are best placed to operate a new high quality service on the route. A final decision will be taken by the Department for Transport.
Simon Earles, Head of Surface Access for Heathrow, said: "Heathrow is already in a better location for passengers and businesses than any other UK airport. Western rail access builds on that strength by cutting journey times dramatically for passengers."
Keith Greenfield, managing director for Heathrow Express, said: "Western rail access is the next logical step for the more than 70 million people a year who pass through Heathrow, and it is also a crucial strand in the plan to secure the future of Heathrow Express."