The telecoms firm wants an integrated approach to its consumer and social media work and for the appointed agency to improve its "brand consideration", a spokesman said.
The spokesman said the pitch process was now closed, following a procurement process that had been running for months, and that a decision would be made on the appointment in the "near future".
Burson-Marsteller was appointed by Vodafone in May 2014, after being named as the company’s preferred bidder.
The Vodafone account has also previously been held by Freuds.
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