The bank formally announced that it was reviewing its ad business earlier this month after splitting with DLKW Lowe, which had been the incumbent on the account for 10 years.
The three shortlisted agencies are now expected to hold initial meetings with Halifax in December, before pitching for the business early in the New Year.
AMV BBDO and RKCR/Y&R already have relationships with various financial brands. AMV BBDO currently handles the advertising for Capital One, Sainsbury Bank and Aviva, while RKCR/Y&R is the incumbent on the Lloyds TSB advertising business, which like Halifax is run by the Lloyds Banking Group.
The process will also mark the first time that Adam & Eve has faced RKCR/Y&R in a pitch since the A&E founders left RKCR/Y&R to launch their new agency in 2008.
Halifax's most recent campaign was set in a fictional radio station called Halifax FM, and featured members of staff broadcasting messages to customers.
Earlier this month, Lloyds Banking Group appointed Santander's Antonio Horta-Osorio as its new chief executive. Horta-Osorio will join the company in March, and will be responsible for all Lloyds brands, including Lloyds Bank and Halifax.