The incumbent is the Havas Media Group-owned Arena, which is understood to have declined to repitch. The agency has handled the business since May 2013.
The review followed Betfair’s promotion of Johnny Devitt to chief marketing officer in May.
Betfair launched the "tap tap boom" campaign in February in the run-up to the Cheltenham Festival. The spot, which was created by WCRS, showed how easy it was to place a bet.
The company spent £28 million more on marketing and customer bonuses in the financial year to 30 April compared with the previous year.
It posted £476.5 million in revenue that year and boasts turnover in excess of £50 million per week.
Betfair, which was founded in 2000, claims to be the world’s biggest internet betting exchange, with 1.7 million active customers. Its headquarters are in Hammersmith, west London.
MediaCom and Betfair declined to comment on the appointment.