This leaves Media Planning Group, Mediaedge:cia and ZenithOptimedia to battle it out for the business.
The statutory review, which takes place every five years, covers all public-service elements of the corporation, including TV, radio, online, sports, factual and learning, and children. Media agencies had been invited to submit a tender via an ad in the Official Journal of the European Communities.
PHD has handled the BBC's media planning and buying account for 12 years.
The winning agency will be announced at the end of March.
Daren Rubins, managing director of PHD, said the agency was sad to see its 12-year relationship with the BBC end: "There's clearly an appetite for change [at the BBC]. We wish them all the best," he said.
Agencies will be responsible for the delivery of media strategy and campaigns, but TV and radio work will be produced by the BBC's usual supplier Red Bee Media, which was known as BBC Broadcast and was its in-house production department until it was sold off in 2005.
In October, the BBC appointed RKCR/Y&R and reappointed Fallon to its ad agency roster.