The agency already handles the bulk of the corporation's £20m ad account and heads the strategy for all of its TV work including BBC One, BBC Two, BBC News, the licence fee and BBC World Service.
It is not yet known whether this latest work for Radio 4 will include radio, TV or press work. No other agencies are believed to have been briefed on the project.
AMV was behind the 90-second commercial for BBC TV featuring a stuntman performing death-defying leaps across city rooftops.
The ad, which broke last April, supported BBC1's spring and summer schedules and was the first offering from the agency since it won the bulk of the BBC business in February 2002.
Radio 4 has enjoyed a growth in listeners in recent months. The latest Rajar figures show its weekly reach was up to 10.03m from 9.7m, while its share of listeners was up from 11.5% to 11.8%.
The BBC currently has two other agencies on its roster, DFGW and Fallon London.
DFGW became the strategic and creative lead agency for children's and sports output last year. It also handles the digital, Proms and Radio 3 strategy and creative.
Earlier this year, Fallon created a campaign for BBC Radio 2 featuring Sir Paul McCartney and REM's Michael Stipe.
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