A deal between Newcastle United owner Mr Ashley and Mr Green is expected to be completed within days.
Ashley's near-69% stake in Sports Direct, which has defied the economic downturn – as rivals including JJB Sports have struggled – is worth more than £1.2 billion.
One source said the price of a 10% stake in Rangers would be "like chicken feed" to Mr Ashley. In 2006, when Rangers was owned by Sir David Murray, JJB signed a £48 million deal to sell the Old Firm club's merchandise on an exclusive basis over the next 10 years.