Broad suffered a shoulder injury during the fourth ODI against India at Lord's, and will also miss the one-day leg of the India tour.
Cook, who won the International Cricket Council's award for the Test Cricketer of the Year at a dinner in central London on Monday, voiced his sympathy for Broad - as well as his own ambition to return to a form of cricket in which he has won just four caps, the last almost two years ago.
"Obviously it's very disappointing for Stuart to miss out," said England's one-day international captain.
"It's gutting for him, but it gives another person a chance to captain England.
"The selectors will make that decision. It's not whether you'd like the job, it's whether you're honoured enough to be given it.'
Cook has already proved his critics wrong by adapting to the ODI format effectively from the five-day game, and he believes he can take it into the shortest format too.
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