Dollond & Aitchison is understood to have shortlisted two agencies for the business.
It is not known whether incumbent Starcom is through to the final round.
Starcom Motive, which was later absorbed into Starcom, won the account without a pitch in 2002, replacing Interpublic's Initiative.
Dollond & Aitchison spent £6,239,802 on media during the year to the end of September, according to figures from Nielsen Media Research.
In addition to Starcom, Dollond & Aitchison uses full-service agencies Delaney Lund Knox Warren & Partners and Principles Communicaitons, as well as direct marketing agency RMG Connect.
Last month, the company teamed up with Sony Pictures Home Entertainment to promote the launch of Spider-Man 3 on DVD.
In January, Dollond & Aitchison linked with Paramount Pictures children's film Charlotte's Web in a four-week push to encourage families to have eye tests.
No one at Dollond & Aitchison was available for comment at the time of going to press.