Anderson, who is England's all-time leading Test wicket-taker, sustained a stress fracture during the home series against Sri Lanka in June, though he did play three Tests against Pakistan in July and August.
England are likely to announce his replacement on Thursday, the BBC reported.
England play three One-Day Internationals beginning on October 7 followed by Tests in Chittagong from October 20 and Dhaka from October 28 before they begin a tour of India, which includes five Tests with the first starting on November 9.
Image: James Anderson during a nets session.
Photograph: Charlie Crowhurst/Getty Images
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