Cook led England to an emphatic 3-0 victory in the first of back-to-back Ashes this year and is expected to lead the tourists to a fourth consecutive test series win over Australia. The first test starts in Brisbane on November 21.
"When I'm asked my opinion I'll tell you what I think and that is Alastair Cook needs to be more imaginative," Warne said in comments published by British media on Monday.
"Alastair Cook can be negative, boring and not very imaginative, still win and be very happy.
"But I think if Australia play well and he continues to captain the way he does I think they are going to lose the series. I don't think he can captain the side like that.
"I think he lets the game drift. He waits for the game to come to him.
"To me I don't like that style of captaincy and when you're playing against the best sides in the world under pressure it won't hold up."
Warne, Australia's top test wicket-taker and second all-time behind Sri Lankan Murali Muralitharan, also took aim at England batsman Joe Root, saying the 22-year-old would be "crucified" by Australia's pace attack if asked to open his team's batting.
"We know Root played well at Lord's but I don't think he is an opener because of his technique and I think Australia found him out," Warne said of the Yorkshire batsman, who scored 180 in the second test at Lord's.
"You can't hang back like that and get stuck in the crease in Australia because of the pace of the wickets.
"He's a good player of spinners and perfectly suited to number six, and in time he can go up to number four and be the main man there.
"It could be crucifying him if he has got to face (Peter) Siddle, (Mitchell) Johnson and (Ryan) Harris on fast and bouncy pitches - he's going to nick off a lot," Warne added, referring to Australia's three pacemen.
Warne also weighed into the controversy generated by Ricky Ponting's autobiography, in which the former Australia skipper admitted concerns about Michael Clarke's leadership qualities earlier in his career.
Ponting's violation of cricket's traditional "keep it in the dressing room" rule has irked past players including former captain Mark Taylor, and Warne went into bat for his close friend Clarke.
"Maybe there was a bit of jealousy, because 'Pup' (Clarke) was batting so well and Ricky was not making any runs," Warne said.
"To me, Michael's very well-respected. The best captains keep stuff in the dressing room. No one ever finds out about it. That's what good leaders are about. So to hear all this in a book is pretty ordinary.
Despite describing Ponting as a "good guy", Warne also slipped in a reminder of the Tasmanian's Ashes record.
"I know he beats himself up mercilessly about being the only Australian captain ever to lose three Ashes," he said.
(Writing by Ian Ransom; Editing by Nick Mulvenney)
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