The company has sent a request-for-proposal to agencies and intends to make an appointment during the autumn.
Byron is handling the pitch itself without an intermediary. It is looking for a brand and marketing agency to work with its in-house team on new campaigns.
Amanda Royston, Byron’s marketing director, said: "Creativity, individuality and idiosyncrasy have been central to the Byron brand from the beginning.
"As the business continues to grow in scale and ambition, we are excited to be looking for a talented group of individuals whom we can partner with and who share those founding values."
Byron was established in 2007 by Tom Byng with backing from Gondola, which owns Pizza Express.
The chain prides itself on selling "proper" hamburgers like those in the US and has 55 outlets across the UK, including 18 in London.
Gondola sold Byron for £100 million in October 2013 to Hutton Collins, which also has investments in Wagamama, the pan-Asian restaurant chain, and the creative agency HeyHuman.