The RMT Union is willing to talk and suspend strike action, threatening to hit Airbourne.
General Secretary Mick Cash said, "We have seen the pre-conditions set out in the latest letter from GTR. The company know that prescriptive pre-conditions would not allow genuine talks to take place.
"In an effort to break the deadlock and get the talks process moving RMT is prepared to suspend strike action set for Thursday and Friday if Southern agree to urgent talks without pre-conditions. The ball is now in their court."
Conductors with Southern have been taking industrial action since Monday (8 August) in the ongoing and bitter dispute over the safety surrounding the introduction of driver-only trains, something due to come into force in 11 days’ time.
Yesterday, Southern also put forward an offer to talk, along with an eight-point plan in an attempt to end the row.
A Southern spokesman said, "We have made the RMT a fair and comprehensive 8-point offer, and we'll meet them any time, any place, anywhere to talk about our offer on our network to settle this dispute. This strike has to stop and has to stop now."