"I don't think he'll be there for the start. He might be ready to do some training, but he won't be ready for the first Test match in India," Cook told reporters.
"I don't know what's happening -- they will be making some decisions over the next seven days or so. I spoke to him last night and he is training well and in good shape physically."
Anderson, England's all-time leading Test wicket-taker, has not played since the fourth Test against Pakistan in August because of a shoulder injury. He has not travelled to Bangladesh, where England tomorrow begin a two-Test series here.
"You should probably speak to the medical team and Jimmy on that. He hasn't yet bowled since, and that has been the problem in the past," Cook told reporters.
"He's making some really good strides and we'll know more later on."
Anderson's continued absence would be a significant blow to England's chances in India, who are the world's number one Test side and have a formidable home record.
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