As Yahoo Inc. shops itself to potential buyers, its core advertising business is weakening. That trend is evident through Craig Atkinson’s ad agency.

Mr. Atkinson is president of ad giant Omnicom Media Group’s PHD unit, which oversees annual ad spending of $4 billion to $5 billion for companies including Starbucks Corp. and Gap Inc. Over the past year, he said, the agency’s ad spending on Yahoo properties is flat to slightly down.

And in the past few weeks, since Carol Bartz was fired as Yahoo chief executive, Yahoo’s Americas-region chief Ross Levinsohn and others have been on a “barnstorming tour” to meet with him and his peers, he said. “They’re saying, ‘We’re willing to do what we have to do to win the business,'” Mr. Atkinson said, adding that while his advertiser clients still view Yahoo as a way to reach and target “enormous audiences,” it’s no longer a “must-buy.”

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