ASLEF held several strikes in December and January leading to the complete shutdown of the Southern network run by Govia Thameslink Railway.
The union joined the RMT in a dispute over driver-only operation, which makes drivers responsible for opening and closing train doors.
A spokesman for ASLEF said: “Further discussions between ASLEF and GTR have taken place today [Thursday] and significant progress has been made.
“We are now in the process of finalising a proposal for agreement.”
Previous deals negotiated by the union’s leadership have been rejected after a ballot of its members.
Meanwhile the RMT, which has raised concerns over safety and access, is due to hold fresh strikes on Tuesday October 3 and Thursday October 5.
THe union is also balloting staff working for Churchill Service Solutions, which holds the contract to clean GTR’s trains.