The organisation has approached a number of undisclosed creative shops with a request for information ahead of a pitch for the business.
Once appointed, the successful agency will devise the identity for the festival, which takes place in October, and outdoor activity promoting it.
Entries are open for this year's festival, although the full programme will not be announced until September.
Last year's festival screened award-winning films such as Precious and The Prophet.
As the online media partner for the festival, Lovefilm last year produced a digital campaign to promote its association with the BFI. As well as a dedicated microsite, blog and social media activity, Lovefilm also used content from its online campaign in its magazine and weekly newsletter.