The advertising agency has struggled to agree a price, according to the Sunday Times.
Tesco hired Goldman Sachs earlier this year to look into selling a portion or all of the business, as part of its efforts to raise cash. In May, bankers estimated a sale price of over £2bn. However, the company is now believed to be valued at £500m-£700m.
Dunnhumby analyses the data behind the retailer’s Clubcard and previous bidders are said to have included US data giant Nielsen.
Both Tesco and WPP declined to comment.