BA announced plans for a new short-haul subsidiary from the airport last month, but parked the scheme following opposition from Balpa over proposed rates of pay.
On Monday (4 October), the national press reported that the airline was set to u-turn on its decision to pull out of the plans after the two parties engaged in "constructive talks".
The conversations with Balpa have now reportedly come to a close.
A BA spokesperson said: "We will now further develop our proposal to provide a full-service short-haul subsidiary operation at Gatwick, offering competitive fares to our customers.
"We will continue discussions with our colleagues, trade unions, suppliers and other stakeholders, following this positive result, and if we can agree a way forward with all parties, we would hope to begin operations next summer."
Balpa acting general secretary, Martin Chalk said the organisation expects the airline to reach a final decision "shortly".
"The British Airline Pilots’ Association and British Airways have concluded an important new agreement covering revised pay and working hours for British Airways pilots operating short-haul operations at Gatwick," he continued.
"This agreement is now BA’s preferred option in relation to the future of short-haul operations at Gatwick. We understand BA is continuing its discussions with other stakeholders with a view to relaunching operations next summer."
