It is understood that the review, which began in March, is for a total of three agencies and that it is expected to be concluded later this month.
Sources told Campaign that Wunderman has been awarded the majority of the work and is tasked with driving digital strategy across all parts of the business.
Wunderman will work with other agencies appointed to BT's digital roster including AnalogFolk which was appointed to head digital content in January.
Karmarama is rumoured to be one of the agencies involved in this pitch.
SapientRazorfish, which has previously been on BT's digital agency roster, said that they declined to pitch.
The win follows Wunderman's appointment to BT and EE's direct marketing account in February.
Wunderman, Karmarama and BT declined to comment on this story.