The company has begun talks with agencies about a small project.
It was previously working with Adam & Eve/DDB, which is not pitching for the business but remains on the Diageo roster.
Adam & Eve/DDB was named the European agency of record for Tanqueray in late 2016 after a competitive pitch process.
Before this the account was handled by Mother, which is also on the Diageo roster and works on the Baileys business.
Diageo and Adam & Eve/DDB declined to comment.