The Manchester agency, which has worked with the struggling supermarket since 2003, won the account after a pitch against JWT Cheetham Bell.
In 2004, BDH was handed responsibility for Safeway's ad business, following Morrisons takeover of its rival.
According to insiders, Morrisons has contacted several agencies in the past few weeks. It is believed to be examining how to move its advertising on from the current "More reasons to shop at Morrisons" campaign, intended to shift brand perception away from its Northern roots.
A Morrisons spokesman declined to comment on the review, adding that the supermarket would not respond to "market rumours".
Since its acquisition of Safeway, Morrisons has focused on converting its former rival's stores, a process which was completed toward the end of last year.
However, Morrisons has been hit hard by rivals and its market share has fallen. For the 12 weeks to December 4, its share was 10.8%, a drop of 1.5% on the previous year, according to TNS.
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