The union's announcement comes after its boss insisted this morning it had not been invited to talks - although transport secretary Chris Grayling said he had written to the union to invite it to the negotiating table, but it had not responded.
If the talks are successful, they'll put an end to pre-Christmas misery for thousands of its passengers, many whom were stranded at home today as Southern entered the first day of two weeks of strikes, expected to stretch into January.
Drivers in both the Aslef and RMT unions are locked in a dispute with Southern's management over the opening and closing of doors, which they say should not be the driver's sole responsibility.
Today Charles Horton, chief executive of Govia Thameslink Railway, Southern's owner, said: "We reached out to Aslef as we said we would and now welcome the opportunity to discuss a way forward with them tomorrow.
"The travelling public are suffering misery and inconvenience and the impact on the regional economy is significant. We assure everyone we are committed to trying to find a solution to the union's dispute."
The move comes after a tense standoff between transport secretary Chris Grayling and Mick Whelan, Aslef's general secretary, following an appearance by Whelan on the Today programme this morning.
In a letter to Whelan dated today, Grayling insisted he had invited him to talks on 6 December, and said he was "disappointed" not to have heard back from Whelan.
"This morning on the Today programme you indicated that you are willing to meet for talks," he said.
"I urge you to call off your strike action and come to the table in a sincere and meaningful attempt to reach a resolution."
Strikes began today after a High Court judge quashed a legal challenge by Southern last week.
The action will take place across the Southern and Gatwick Express networks tomorrow and Friday, as well as on Monday and Tuesday, and for a full week between Monday 9 January and Saturday 14 January, with the unions taking alternate dates.
Yesterday Southern urged commuters not to travel, which induced vociferous complaints from its passengers.