The 5th and final Test of the series will be played at Chennai's MA Chidambaram Stadium from tomorrow. India have already won the rubber 3-0.
"It is a bit of everything, ankle and shoulder. A bit of bowling soreness. We are trying to look after him," Cook was quoted as saying by "BBC" on Thursday.
Anderson missed the 1st Test due to shoulder injury and joined the squad to play the next 3 matches. In the last Test in Mumbai, he was in the news for criticising Virat Kohli's batting technique despite the Indian captain scoring a career-best 235.
"I'm not sure he's (Kohli) changed. I just think any technical deficiencies he's got aren't in play out here. The wickets just take that out of the equation. There's not that pace in the wicket to get the nicks, like we did against him in England - with a bit more movement.
"When that's not there, he's very much suited to playing in these conditions. He's a very good player of spin - and if you're not bang on the money and don't take your chances, he'll punish you," Anderson, England's leading Test wicket-taker, had said.