England are trailing the five-match series 0-3 after losing the fourth ODI by nine wickets against India at Edgbaston.
"At this precise moment in time, no," said Cook when asked whether he will relinquish his ODI captaincy.
"I will be the captain of this team in the World Cup if I'm allowed to be. I don't have a say on selection but I've captained for three-and-a-half years with the goal to try to win the World Cup in Australia.
"I know that seems a bit far-fetched at the moment when we're losing games of cricket but there are a lot of really good players in that change room and if we can improve at the rate we need to improve. We've got a chance and that's what we have to believe in," he said.
England's batting collapsed once again and scored only 206 runs before they were bowled out in the 50th over of their innings.
India then chased down the target with 19.3 overs to spare with Ajinkya Rahane (106) scoring his maiden ODI century and putting up 183 runs with Shikhar Dhawan (97 not out) for the opening wicket.

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