International Nuclear Services is seeking an agency for a three-and-a-half-year brief worth £500,000.
As part of the company's 'global acceptance activities', it is looking for an agency to engage with academics, politicians and journalists to reduce the amount of controversy generated by the trips.
Sellafield, the nuclear reprocessing site in Cumbria, is among the sites where the company picks up waste.
The news follows the return to operation last weekend of Japan's Ohi nuclear plant. The country shut down all of its reactors for safety checks following the Fukushima disaster last year.
Ben Todd, comms manager for International Nuclear Services, said the brief was 'very wide-ranging and complex' and required a high degree of specialist knowledge in the nuclear and maritime industries.
He added: 'We have invested an enormous amount of effort telling our story on the front foot over many years with these en route states, and we expect the success we have had so far to continue.'
The winning agency will be expected to engage with stakeholders in countries situated along the shipping routes, including academics, politicians, government officials, journalists and NGOs.
One of its tasks will be to emphasise the safety measures deployed around the journeys, which also take on spent fuel in La Hague.
The brief states that the winning agency must have had experience of dealing with 'political and media' issues in countries including South Africa, the US and New Zealand.
The pitch comes as US-based agency Gavin Carter & Associates' contract with International Nuclear Services comes to a close.
International Nuclear Services has offices and facilities in the UK, France, Germany and Japan.