The brief is due to be issued imminently and the pitches are planned to take place at the end of July.
Campaign reported last week that Lloyds Bank has selected Adam & Eve/DDB to work on its 250th anniversary activity without a pitch. It is understood that the agency is tasked with bringing back the black horse mascot.
RKCR/Y&R picked up the Lloyds Bank account in 2002. Before this the business was handled by Saatchi & Saatchi.
Halifax, which is owned by Lloyds Banking Group, appointed Adam & Eve to its £25 million ad account in 2011. The shop fought off competition from RKCR/Y&R in the pitch.
A spokesman for Lloyds Banking Group said: "We would never comment on future campaigns."