The two sides adjourned talks after two days of discussions on 24 and 25 April.
The row is over Southern's plans to give drivers responsibility for door operation and changing the role of guards to on-board supervisors.
The RMT has taken 31 days of strike action over the proposed changes.
A spokesman for Southern said: "I can confirm we will be meeting with the RMT next week but, at this stage, can't confirm the date."
In a separate dispute, members of drivers' union Aslef rejected initial proposals to resolve the row in February and this month voted against another proposed deal.
Southern rail and the RMT union are to continue negotiations next week in a bid to resolve a year-long dispute over driver-only operated trains.