"I'd keep him as captain because we're close to the World Cup. It's important from a leadership point of view," Giles said.
England lost the recently-concluded ODI series against India 1-3 and Cook's future is a major talking point ahead of the seven 50-over matches against Sri Lanka in November and December.
Giles, who was England's ODI coach from 2012 to until earlier this year, said Cook's position could become "untenable" if another series is lost.
"The seven one-day games in Sri Lanka are so important," he said.
"Winning there is very difficult, so if the weight of pressure and the public opinion against Cook continues to rise then his position could become untenable by the end of that series."
Giles said Cook might have faced the axe as Test captain too had it not been for a couple of decent knocks against India before the ODI series.
"If (Ravindra) Jadeja had taken that catch at Southampton when Cook was on 15 we might already have a new captain – but it's too late to change it now," said Giles.
"Cook deserves a bit of time but he's not playing well - he's just beating the ball up; he's not caressing it, not timing it. He could use his feet more and be a bit more pro-active and that is the Alastair Cook I have seen play well in one-day cricket," he said.

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