The Olympiakos goalkeeper played under the Scot for four years from 2001 until 2005, and he does not believe success at Old Trafford will dry up when the 71-year-old departs
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Current Everton boss David Moyes is expected to replace Sir Alex, and Carroll, who played for United from 2001 until 2005, believes the infrastructure at the club is strong enough to guarantee success for the next decade.
Carroll told talkSPORT: "Personally I don’t think that dominance will end because there is such a good team there at Manchester United, even with Sir Alex Ferguson moving upstairs.
“OK, there are a lot of things happening but Manchester United are going to be a strong outfit for the next five to ten years.
“I think everything has just been built around what he’s done and what he has done at youth level with all the young players and what he’s done with the training ground, it’s fantastic.
“He’s put everything in there and [they’re] ready to move on. In football you have to move on.”