The union's general secretary Mick Whelan said: "I am today proposing a new process to find a resolution to our industrial dispute with Southern."
Whelan added: "Aslef believes that the best way to resolve the dispute at Southern is for all parties to engage in meaningful talks - without preconditions - aimed at finding an agreed way forward."
Strike action by the Rail, Maritime and Transport (RMT) union and Aslef has caused disruption on the network over a series of months, as a dispute over the role of the guard remains unresolved.
The RMT has a walkout planned for Monday 23 January, while Aslef had more planned on the 24, 25 and 27 January. It has suspended all action on Southern rail for next week.
The RMT said its strike remained on, but that it had written to the TUC asking to be involved in the same process.
"RMT is awaiting a response to that request," a spokesperson said. “In the meantime, the scheduled action in the Southern guards dispute remains on.”
Southern's parent company Govia Thameslink Railway (GTR) accepted the union's request for fresh talks, which will be held at Trades Union Congress (TUC) Congress House from tomorrow.
Chief executive Charles Horton: "We've always made clear our willingness to engage in meaningful talks with Aslef to find a route forward to end their dispute.
“So, together with our passengers and businesses, we warmly welcome their decision to suspend next week's planned industrial action. This is an important and significant development for the travelling public and the regional economy and our focus and efforts now will be on productive talks with the union and trying to find a solution and a way forward."
GTR has said it will make no further statement or comment until the talks have concluded.
The general secretary of the TUC, Frances O'Grady, said she was "ready to play a part if we can help" and called the news an "important development".
I & the TUC are ready to play a part if we can help. Glad to have been approached by ASLEF in important development https://t.co/RKic7DGAsJ— Frances O'Grady (@FrancesOGrady) January 17, 2017
It comes after the train firm had said it intended to take the union to Supreme Court over the industrial action, after an initial attempt to halt the strikes through the High Court failed in December.
A GTR spokesperson said: "Whilst we've submitted our application to the Supreme Court, our focus is now on finding a solution through these talks to end the dispute."