The measures were outlined in a draft airports national policy statement (NPS), published February 2, and opened to a 16-week UK-wide public consultation.
The measures are included in a draft national policy statement (NPS) setting out why Heathrow expansion is the Government's preferred option for boosting airport capacity in south-east England.
Currently, eight United Kingdom airports have links with Heathrow but ministers want to expand domestic connections.
In a statement to Parliament, announcing the start of consultations over the plans to construct a third runway at Heathrow, Mr Grayling said the Government expects Heathrow to add six more domestic routes across the United Kingdom by 2030, bringing the total to 14, strengthening existing links to nations and regions and also developing new connections.
An additional 260,000 take-offs or landings would be permitted each year from the expanded airport, on top of the current cap of 480,000.
By now you may have heard the government has set out its draft national policy statement for Heathrow expansion, kicking off a 16-week consultation.
An earlier report by market research firm ComRes found that 74% of 130 MPs surveyed backed a third runway at London Heathrow.
"By backing the north-west runway at Heathrow airport and publishing our proposals, we are sending a clear signal that when we leave the European Union, we are open for business", Mr Grayling will say, according to advance extracts of his speech.
There will be information events held near Heathrow and across the UK.
"It is a tribute to all who work at Heathrow, including the many thousands of Unite members, that it will continue to develop, and in view of the UK's need to recast its relationships with the world following Brexit, this is a much-need investment for the national economy".
This will influence decisions taken later in the planning process for a third runway at Heathrow. A final proposal is expected to be submitted to the Planning Inspectorate as part of an application for a Development Consent Order in the summer of 2019.
Heathrow expansion will provide unrivalled connectivity to new and emerging markets, boosting worldwide trade and cementing London's role as a true outward-looking global city.
The runway, if approved, is not expected to be operational until around 2025.
Tony Hallwood, its aviation development director, said: "Expansion of the UK's hub will boost businesses across the Leeds City Region, by attracting investment and reaching key worldwide markets from Yorkshire via our direct connection to Heathrow".