"(It's) really good news about Anderson. He has worked hard to get back. He's got the all clear. Just chatted with him yesterday and the day before. (Him playing in the) second Test (at Vizag) is a good possibility. We will know more after seeing how his body reacts," said Cook at his first media meet here after landing in India three days ago with his team.
"James Anderson will join England's Test squad in India next week, and is increasingly hopeful of playing a significant part in the five-match series after making encouraging progress in his recovery from a shoulder injury," according to the ECB website.
34-year-old Anderson, England's highest Test wicket-taker (463), missed the drawn (1-1) series in Bangladesh prior to the team's arrival here because of a stress fracture in his right shoulder. He has not played since against Pakistan at the Oval in mid-August.
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Cook said the vast experience Anderson has of Indian conditions will be very handy.
"His experience of these conditions and the number of wickets he has got in all types of conditions will only help the other guys."
Asked about lack of match practice for the 119-Test veteran as he heads to India straightaway to take part in a gruelling series, Cook conceded it was not a perfect scenario.
Team's head coach Trevor Bayliss also felt Anderson's arrival will boost the team.
"To get anyone back with that experience and that many wickets will be very good for everyone. He has the experience of bowling in these conditions," said Bayliss.
For the record, Anderson has toured India in 2006, 2008 and 2012 to play Test matches and he has taken 22 wickets in seven games combined during those visits at an average of 29.81, as against his career average of 28.28 per victim.