The move comes 21 months after Miles Calcraft Briginshaw Duffy quit the account citing creative differences. Dyson subsequently took all of its advertising in-house.
A number of top 20 UK agencies are understood to have been approached as Dyson prepares to launch more products to sustain its leadership of the UK market.
Senior executives are seeking an agency to provide the right cultural fit at a time of intensifying competition.
In January, arch-rival Hoover appointed Rainey Kelly Campbell Roalfe/Y&R to launch a state-of-the-art upright cleaner in a direct challenge to Dyson.
Dyson's last TV campaign appeared in April. Two 30-second spots featured people using the company's products in real-life situations.
Creative work for the campaign was produced by the art director Tony Muranka, working alongside Dyson's marketing team. Media was handled by Walker Media.
Dyson claims a 45 per cent share of the UK floorcare market, but believes there is room for improvement.
It has been a significant UK advertiser since 2000, when MCBD drafted in David Abbott, the Abbott Mead Vickers BBDO founder, to work on its first campaign.