The colourful entrepreneur is in advanced talks to sell the stake in the high street chains to Leonard Green & Partners for as much as £250m (€308m).
A source close to the deal, which is not finalised but is expected to be announced tomorrow, said it would give Green a powerful war chest to "buy, deal and expand around the world".
The retailer, estimated to be worth £3bn, is driving an ambitious international expansion programme in America and Asia.
The deal also offers Green an alternative way of taking money out of his empire than as a dividend from Arcadia, the holding company that owns both brands as well as Dorothy Perkins, Burton, BHS and Miss Selfridge.
In 2005, Arcadia attracted controversy by raising debt to pay a dividend to its legal owner, Lady Green, the tycoon's Monaco-based wife.
Under the terms of the deal – first reported by Sky News – Arcadia would ring-fence the remaining stakes in Topshop and Topman from its other fashion business, which include Dorothy Perkins, Burton, BHS and Miss Selfridge.
Arcadia, which employs 43,000 people, recently reported a rise in pre-tax and pre-exceptional profits from £133m last year to £167m in 2011.
It does not report a breakdown of the performance of its individual chains but analysts say Topshop is the most profitable part.
Arcadia has bank debt of £308.9m and net debt of £445m.
Group debt peaked after the controversial dividend payment but two years ago Green vowed that the group would be debt-free by this year. At the time he said the debt would be cleared by the rapid growth of the company.