The move follows news of a Dreams creative review, called last month.
The Newcastle-based full-service agency Robson Brown is the incumbent on both creative and traditional media planning and buying for Dreams, while Brilliant Media handles digital media.
The retailer has talked to a number of media agencies about the business. It plans a separate media pitch process ahead of a planned appointment in November.
Dreams, which has more than 200 stores throughout the UK, is understood to be keen to highlight its niche expertise as a specialist bed retailer, with consumers increasingly turning to multi-purpose retailers such as Argos and John Lewis when purchasing beds.
Robson Brown, which also has offices in Manchester and London, started working with Dreams in 2000. Since then, the company has significantly upped its media spend and Robson Brown last defended the business in a competitive pitch in 2006.
The retailer has sponsored the past two seasons of Celebrity Big Brother, and has also been a sponsor of the ITV drama Heartbeat, using the strapline: "Everything for a great night's sleep." Other TV dramas sponsored by Dreams include ITV's Doc Martin, starring Martin Clunes.