David Ross, who also serves as financial adviser to the Olympics for London mayor Boris Johnson, could face an investigation by UK regulator the Financial Services Authority over the deals, the Independent stated.
Under stock market rules, directors who use company stock against loans must publicly disclose the deals within four days of their completion.
The publication added that Mr Ross is believed to have used his holdings in other companies to guarantee further loans.
In a statement, Carphone Warehouse said Mr Ross used his company shares against credit between 2006 and 2008. None of the loans have defaulted and Mr Ross intends to retain his holding in the company, it added.
Charles Dunstone, who founded the retailer with Mr Ross in 1989, described his resignation as a "great personal sadness".