Workers are set to walk out again for 48 hours from this Sunday, then for a further 24 hours on August 11, and over the weekend of August 13/14.
The union opposes any extension of driver-only trains and wants guards to be in control of operating doors, stating safety is at the core of the dispute.
The company earlier wrote to the RMT to challenge some actions it believe contravened the legislation that governs industrial action.
The union said the company had suggested retaining conductors on trains as a “way forward” to resolving the row.
In a circular to members, RMT general secretary Mick Cash said: “ScotRail has confirmed that we are considering a way forward whereby conductors will be retained on EMUs [electric multiple unit] in the network area.
“It is proposed that any ScotRail EMU services that operate on those routes that are being electrified, now or in the future, and services that operate on the North Berwick-Edinburgh-Carstairs-Glasgow routes (ie excluding any EMU services currently operating under existing driver only operation arrangements) will be guaranteed a conductor on every new electrified train; and guaranteed that the conductor will retain their full competency (rules, track safety, evacuation).
“In addition ScotRail confirm that trains operating these services will not run without a competent conductor on board.
“This proposal, including the above guarantees, is subject to ScotRail and the RMT entering into discussion about and agreeing a method of train dispatch for these services.
“Once this proposal and the method of dispatch are agreed it will be adopted for the Abellio ScotRail franchise and will apply beyond.”
The current programme of industrial action remains on, the union added.
A ScotRail spokesman said: “At yesterday’s meeting with the RMT we discussed a proposal that would see a conductor retained on the new electric trains when they enter service next year.
“It would also mean a change to the way in which those trains are dispatched.
“We were encouraged by the talks today but further discussion will need to take place.
“In order to enable this, we have asked the RMT to suspend all upcoming strikes and to encourage a return to normal working.
“We have always said that there was a way forward on this issue. Our priority has always been to do what is right for our customers and our people.
“We are investing hundreds of millions of pounds in new trains and over a billion pounds in electrifying lines.
“This will transform the way people travel. The way in which we work has to keep pace with that change.”