BBH is the incumbent, having won the account from JWT five years ago.
A spokesperson for Diageo said: "We can confirm we are currently undertaking a review of Baileys global advertising, this is in line with standard Diageo review processes. We are talking to a number of agencies, including BBH, the incumbent agency."
BBH's hold on the Diageo roster weakened in 2006 with the loss of its £20m Smirnoff account to JWT.
Diageo reassigned the Smirnoff business to allow BBH to continue to work with InBev, although the agency also continued to handle creative work for Diageo's Johnnie Walker and Baileys.
If BBH loses Baileys, Johnnie Walker will be the only Diageo brand it continues to work on.
The Baileys account, including the flagship Baileys Irish cream liqueur brand, is estimated to be worth £7m in the UK.
Sharon Keith, Baileys global brand director, will lead the review.
BBH was unprepared to comment at the time of publication.
Earlier this month, Diageo said that it was cutting back on new product launches as part of its five-year innovation plan. Its future strategy is to "test more and launch less".
Diageo's most recent successful brand extension has been that of Baileys Flavours variants; Mint Chocolate and Creme Caramel.
This article was first published on brandrepublic.com