Scotland's Transport Minister is "hopeful" a new offer will resolve a pay row which has led to a big cut in ScotRail services.
An improved deal of 4.2% is to be considered by members of the Aslef union.
The dispute has resulted in train drivers refusing to work on rest days or on Sundays and has triggered a wave of cancellations.
A new, temporary timetable has seen a third of services scrapped - leading to misery for thousands of passengers.
The BBC reports that Transport Minister Jenny Gilruth said yesterday the industrial dispute had led to a "challenging time" for ScotRail, which was nationalised last month.
Asked if a resolution was near, Ms Gilruth said: "I'm hopeful."
She added that the offer was a good one, but it was now up to the union to decide whether to accept it.
Ms Gilruth said: "I know that Aslef and other trade unions in rail want to make public ownership a success. So, moving forward, I'm really keen to work with them on how we do that.
"Getting a resolution here is absolutely essential."
Economist Tony Mackay has estimated the pay row could cost the Scottish economy between £75million and £80million every week from a combination of the fall in economic output and extra money having to be spent by travellers to get to their destinations.
Aslef's Scottish organiser, Kevin Lindsay, has said the improved pay offer would be put to members for their consideration.
But no quick end to the dispute is expected as the union's full consultation is likely to last up to four weeks and will be followed by a formal vote.
During topical questions at Holyrood on Tuesday, Tory MSP Graham Simpson asked what contingency plans the government had in place should train drivers reject the latest pay offer, in light of the cancelled services at the weekend.
Ms Gilruth told MSPs the temporary timetable was delivering a "reliable service moving around 90% of passenger numbers prior to the current disruption".
She added that additional late-evening services were added on Friday and Saturday, but acknowledged passengers had been left "inconvenienced and frustrated".
The transport minister also said the operator would continue to look at what more it could do to improve the availability of weekend services.
But Mr Simpson responded by highlighting that a union ballot would take three weeks and lead to "nearly a month of disruption to start with".