England begin their five-match one-day series in Rajkot on Friday looking to win in India for only the second time - their last two attempts, in 2011 and 2008, ended in 5-0 defeats.
Several of the current squad are not first-choice picks but the captain has told them a place at the Champions Trophy, held in England this June, could still be on offer, saying: "I don't know how many places are up for grabs but I would say a lot of them are. I think there's a chance if people perform well and they've got the shirt at the moment."
He added: "That's what you want, you want competition and people pushing hard to put the people who are in the team now out.
"Performances from people on this tour, if they perform really well, will mean it's really hard to leave out a player."
England have plenty ahead of them before the International Cricket Council's 'mini World Cup' lands on their doorstep, with the ongoing series, a trip to New Zealand and a return visit from the Black Caps all to be contested.
But Cook makes no apology for highlighting the importance of a major tournament on home soil.
"I think it's a very important trophy," said Cook.
"We haven't won an ICC 50-over tournament as an England side. So, as a group of players we've got an opportunity at home, in our conditions which we're very comfortable in, to try to win that. I think it's very high on my shopping list."
- Sports & Recreation