The brand has already approached agencies with a view to holding a pitch for the business later in the year.
JWT has held the account since April 2008, when it beat Leo Burnett and Bartle Bogle Hegarty, the previous incumbent, to win the business.
The agency's relationship with Smirnoff, another Diageo brand, is unaffected.
News of the pitch follows Diageo's appointment of Philip Almond as the new global brand director for the Baileys brand. Almond, previously the UK marketing director at Diageo, took on the role in August last year.
JWT has produced some high-profile ads for Baileys during its time working on the business. Its last work was a TV spot called 'Treat Yourself Tonight', which featured a close-up of a woman's lips as she sung the song 'Night And Day' by Ray Charles.
The agency also created another TV ad that saw Baileys being splashed on to a woman's lips. It hit the headlines after some viewers complained that the content was close to the imagery found in some pornographic films.
Earlier this year, Baileys announced that it had signed a deal with Channel 4 to sponsor the new series of 'Desperate Housewives'.
Baileys' relationship with its other roster agencies – Carat, Agency Republic and Chemistry – is unaffected by the review.