M&S chief executive Stuart Rose has been in talks with Green, a friend and former colleague, for a number of months, according to sources.
The two men met to discuss the job after Christmas and two additional meetings with M&S senior management took place more recently.
Last November, Green set out grand plans for Tesco's fashion range to bring down high street giants M&S, Next and Topshop. He said that Tesco would invest millions in an expanded range of upmarket clothing to be sold in specific areas of its supermarkets. News of his decision to quit will come as a blow to Tesco boss Sir Terry Leahy.
Green is expected to hand in his notice to Leahy this week. His new job is likely to mean a large pay rise for Green.
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