The incumbent will pitch against Soul, which handles Drambuie Cream Liqueur.
The drinks brand is also thought to have approached other undisclosed agencies.
The review comes as part of a relaunch of the Drambuie Liqueur brand, which involves repackaging and repositioning. The company is diverting investment from the US, where it has been heavily backing its Cream Liqueur brand, known as Drambuie Silk in the US.
The brief, which is supported by a £4 million budget, covers advertising to back the brand's relaunch in a number of markets including the UK, Greece and the US.
Burkitt DDB has held the Drambuie Liqueur business for more than five years. Recent work from the agency included a poster campaign in November that aimed to broaden the drink's appeal to 30- to 40-year-olds. The ads focused on the social aspect of liqueur drinking as an all-evening tipple, challenging pre-conceptions that Drambuie is only an after-dinner drink.
It also developed a TV campaign called "cab driver", in which a cab driver is seen trying to amuse himself while he waits outside a dinner party because the couple that ordered the taxi are having such a good time that they have forgotten about it.
Soul picked up the Drambuie Cream account in 2002, two years after the brand was introduced into the UK. The product targets a younger audience to Drambuie Liqueur and is positioned to compete with Baileys.
Drambuie is distributed in the UK by Bacardi Martini, which took over the business in 2002.