Known as "Boris Island" because of London Mayor Boris Johnson's backing, it was one option being considered by the Airports Commission on how to expand airport capacity in the UK.
If given the go-ahead, the plan would have meant the closure of Southend Airport.
An official announcement is expected on Tuesday.
Earlier, the Financial Times reported that Whitehall had confirmed the "Boris Island" plan would be ruled out.
The commission, led by Sir Howard Davies, was set up by the government to consider ways of expanding the UK's airport capacity. Its final report is expected next summer, after the general election.
The decision to eliminate Boris Island as an option would leave the commission with three alternatives: Adding a third runway at Heathrow, lengthening an existing runway at Heathrow, and a new runway at Gatwick.