The brag of the RMT obstruction national has said that some sides progressive successful the long-running quality implicit wage and jobs request to "work quickly" to extremity the strikes.
Mick Lynch told the BBC that determination had been "an speech of views", but it was important that employers, ministers and unions were getting together.
He said helium would similar to spot improved proposals connected wage and moving conditions for its members.
But helium told Sky News that helium believes a woody is "achievable".
"We request to enactment quickly, and we request a spot of goodwill from each parties," Mr Lynch said.
On Friday, obstruction workers began different 48-hour walkout pursuing strikes earlier this week.
There is besides concern enactment scheduled from 18:00 connected Christmas Even until 27 January arsenic good arsenic strikes successful aboriginal January.
Rail passengers are being advised to question lone erstwhile perfectly indispensable and important disruption is besides apt connected non-strike days.
Asked however overmuch of a wage summation would beryllium capable for RMT national members, Mr Lynch declined to springiness a fig but said: "We'll sermon that down closed doors with the employers.
"We've asked for important summation successful pay. We don't enactment a fig either publically oregon to the employers successful our claims."
The national person besides said that the wage connection which helium would picture arsenic "acceptable" would beryllium connected the conditions attached.
"The authorities is insisting that each this wealth is aforesaid generated from our ain members' moving practices truthful it depends what tin beryllium generated done the savings and efficiencies they're demanding," helium said.
"It's not arsenic analyzable arsenic maine saying 'I'd similar this magnitude of money' and them saying we'll spot what we tin do, unluckily it's precise complex."
The RMT is progressive successful 2 sets of negotiations.
One is with Network Rail, wherever the RMT represents astir 20,000 signallers and attraction workers. The different is with the Rail Delivery Group (RDG), wherever it represents astir 20,000 workers astatine 14 bid companies.
Along with the wage rises, Network Rail, which owns and operates the tracks crossed Britain, offered its unit different benefits including discounted obstruction question for household and friends.
But the woody besides depended connected large changes to moving practices successful its attraction teams, which would impact 1,900 occupation losses, though Network Rail has insisted this could beryllium achieved by voluntary means.
The institution has said determination would beryllium a warrant of nary compulsory redundancies until the extremity of January 2025.
Mr Lynch besides deed retired astatine claims from obstruction institution bosses that changes to moving conditions and schedules would not compromise unit safety.
"At the infinitesimal we person planned preventative attraction which ensures we person a harmless regime. They're going to determination to risk-based attraction which means 50% of the existent level of inspections and attraction enactment volition beryllium cut,".
"So there'll beryllium fractional the enactment getting done compared to antecedently and we judge that compromises safety."
He suggested that much nighttime shifts being required for workers would besides person a atrocious interaction connected their wellbeing.