The pitch process is being handled by agency-client intermediary, AAR.
77PR won Nintendo's consumer account in 2013. Fishburn has handled the gaming company's European PR and corporate comms since 2008.
PRWeek understands that Fishburn will continue to hold the EU and corporate account. It is unknown whether the agency is repitching for the consumer work.
The pitch is being overseen by Nintendo UK head of comms Jo Bartlett.
Nintendo UK said: "In order to keep the PR activity for Wii U and Nintendo 3DS both fresh and innovative, Nintendo UK is currently reviewing its UK PR agency with the help of the AAR. Nintendo is in the final stages of the process."
AAR declined to comment.