The company, which is owned by entrepreneur Surinder Arora and is one of the largest landowners at the airport, has lodged a DCO scoping report for its expansion plan with the Planning Inspectorate's (PINS's) major infrastructure team.
It said it intends to submit a DCO application, under the streamlined Planning Act 2008 regime for major infrastructure, "in due course".
Heathrow Airport Holdings has already proposed its own plans for a third runway to the north-west of the existing airport.
The operator submitted its own scoping report to PINS in May last year and said it expects to lodge a DCO application in 2019/20.
Last May, Arora Group revealed its rival ‘Western Hub’ expansion plans, which it claimed would be cheaper and less disruptive than the airport’s own proposals.
The following month, the government published its Airports National Policy Statement (NPS), which confirmed the government’s desire to see a third runway built at Heathrow.
Arora’s scoping report states the company "believes there is a better way to deliver the increased capacity at Heathrow Airport identified in the Airports NPS" and describes its rival plan as "a new, more efficient approach to Heathrow Airport expansion".
The project "will provide terminal facilities to enable the delivery of at least 260,000 air transport movements per annum, which is an accordance with policy on the expansion of airport capacity at Heathrow Airport as set out within the Airports NPS," it says.
Any plan to expand Heathrow Airport will face a series of hurdles before planning permission can be granted, not least the objections of local authorities in the area.
By August 2018, a total of six applications seeking to overturn the airports NPS had been lodged at the High Court by councils and campaign groups.
A Heathrow Airport spokesperson said: "Heathrow expansion is an opportunity to connect all of Britain to global growth and the Department for Transport has stated that Heathrow Airport Limited is the only credible promoter of the expansion programme.
"The Arora Group’s plan appears to solely be about building a new terminal which will not deliver on the commitments we have made to Britain and our local communities."