"He might come out to do some training but he will not be ready to play in the first test," Cook said.
"I spoke to him last night. He has been doing a lot of training and is in good shape physically. The decision is going to be made over the next week on that (when he goes to India).
"The test for his body is when he starts bowling, but he is making some strides."
Anderson, 34, has struggled with injury this year and missed the first test against Pakistan at Lord's with a shoulder injury before it flared up again at the end of the domestic season.
The first of five tests against India starts on Nov. 9.
Cook will overtake Alec Stewart to become the most-capped England test player when he steps out for the first of two tests against Bangladesh on Thursday.
"I started however many years ago and you never thought you'd get anywhere near, so to break the record like that is very special," he told the England and Wales Cricket Board website ahead of his 134th test.
"A lot of luck, I suppose, is needed with injuries and all that stuff and to score just enough runs at the right time to keep yourself in the team," said Cook who rejoined the squad in Chittagong after returning home for the birth of his second daughter.
(Reporting by Martyn Herman and Amlan Chakraborty; editing by Nick Mulvenney)
