It is understood that both Rapier and Kitcatt Nohr Alexander Shaw are pitching for the business, although a number of other DM shops have also been approached.
Although the retailer, which is enjoying massive growth on the high street, already promotes its stores via inserts in weekend supplements, it has never run a wide-ranging direct marketing campaign.
The move follows the recent appointment of Gill Barr as the interim marketing director. She took over from Andrew Woodward, who left the retailer at the end of last year.
Kitcatt Nohr, Rapier and John Lewis were unavailable for comment.