Material including fuel containing highly enriched uranium could be transported from Dounreay in Caithness to Sellafield in Cumbria.
The move is one of two options put out for public consultation by the Nuclear Decommissioning Authority (NDA).
The other option is to continue to deal with it at Dounreay.
The material is classed as "exotics" and separate from tonnes of breeder material to be moved by rail from Dounreay to Sellafield later this year.
In a newly-published consultation document, the NDA said the "exotics" could be moved in up to 60 journeys over six years starting sometime in 2014 or 2015.
The mode of transport has not been determined at this stage.
The NDA plans to make a decision on the material in March or April.
Its preferred option is to transport the "exotics" by road or rail to Sellafield where there are existing facilities, or ones being built, to handle it.
Doureay's storage sites will have to be upgraded or replaced within the next 15 years, according to the NDA.
The authority added that it would take eight to 10 years to design and build the necessary facilities.
Dounreay, an experimental nuclear power site, is being demolished and cleaned up.
There are three groups of "exotic" material that needs to be dealt with at the site, or transported to Cumbria.