Members of the Rail Maritime and Transport union are due to walk out on Saturday and again on Christmas Eve in a row over the dismissal of a colleague, threatening travel chaos for passengers over the busy festive period.
RMT members on the firm's sleeper services are also set to strike for 24 hours from the evening of December 21 and again from the evening of December 23.
The planned action is in support of Scott Lewis who was dismissed after an incident over the type of ticket issued to a member of the public.
A union spokesman said: "Following further dialogue between RMT and ScotRail the union is in receipt of a formal offer from the company aimed at resolving the current dispute. That offer will now be considered by RMT's executive first thing on Wednesday morning."
A spokesman for the train operator said: "ScotRail today confirmed that constructive dialogue has taken place with the RMT to avert strike action next weekend and to end the dispute."
The spokesman said it was hoped there will be a successful outcome and that a formal response from the union will be received tomorrow.
"Given the circumstances, ScotRail will not be publishing its contingency plans today. To do so would only cause confusion while a formal offer to end the dispute has been made."