The company is looking for a shop to revitalise its entire approach to advertising, and to create a new strategy for its marketing communications.
Despite asking agencies to come up with new material, it is understood that Miele has already briefed its incumbent - the Horsham-based agency Ethos - with the task.
The German business has plans to alert other agencies if Ethos fails to deliver.
Jenny Taylor, the marketing services manager at Miele, said: "If Ethos doesn't come up with something we like, we will then go out to pitch.
"We have given it a few weeks to tackle the brief, so we'll just have to wait and see what it comes up with."
Ethos was appointed in February this year, following a pitch against a number of other local agencies.
Miele manufactures a wide range of white goods, including washing machines, tumble dryers, dishwashers, fridge freezers, hobs, hoods and coffee machines.
Its latest advertising push, a digital campaign called "miles better", was launched in March this year. It was created by the Laud Group, which picked up the brief after a five-way pitch. It used social networking sites to encourage users to push the brand via word-of-mouth.