Twenty Twenty Media Vision, set up by MediaCom founder Bill Jones, s, which includes national and regional press, since March last year, when it took the brief from fellow Tunbridge Wells-based media agency WFCA.
Carpetright has already had preliminary conversations with several, unnamed media agencies, in advance of pitching the account.
Brilliant Media currently holds the TV and radio-buying account for the brand, which is understood to be part of a consolidated briefing to the agencies that have been approached.
Both incumbents expected to compete for the brief should it go to a full-blown pitch.
The retailer, which is set to unveil its full-year profits tomorrow (Tuesday), has issued three profit warnings over the past 12 months and is expected to announce 2010 profits just below the £17m it recorded in 2009.
The group was founded by Lord Harris of Peckham and has 560 outlets in UK and Ireland, and a further 120 in the Netherlands and Belgium.
It now has 230 shops selling the Sleepright brand, as the retailer attempts to move towards new revenue models.
A spokesperson for Carpetright said the approach to media agencies was part of a "market test".
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