The company said it had written to the RMT union inviting it to recommence ACAS talks.
Northern says the union has accepted but it is unclear when talks will resume.
It follows a suggestion by the union they could call off the series of weekend strikes that have blighted the region's transport networks.
However, tomorrow's timetable - which had been severely affected by strike action - will not return to normal, with Northern citing a lack of time to reinstate full service.
Northern spokesperson said: “Northern has invited RMT to talks at ACAS in order to resolve its dispute.
"We are pleased that RMT has agreed to recommence talks at ACAS with no pre-conditions and we look forward to resolving this long-running dispute.
"Those talks can build on recent public statements made by Transport for the North and Department for Transport on the customer service and other benefits that will come about with a second person retained on Northern services in the future.
"We want to make it clear to customers that the timetable for tomorrow, Saturday 01/12/18, cannot now be changed because it takes a number of days to reinstate a normal timetable. Regardless of whether RMT continues its dispute tomorrow, the Northern service tomorrow will be the revised timetable of around 700 services, between 8am – 5pm.”