The account is currently held by Walker Media and the pitch process is being handled by the AAR.
The technology company has agreed on a shortlist to pitch for the business, which includes the incumbent.
Dyson said in a statement that the review was "part of a standard company process" and that a decision was expected in the summer.
In addition to vacuum cleaners, Dyson has expanded into hand-dryers and launched a bladeless fan last October.
The review follows last month's announcement by Sir James Dyson, the founder of company, that he is seeking to double the number of engineers working on research and development projects.