Rio Ferdinand is fit and Nemanja Vidic has returned during pre-season from a long-term knee injury sustained in December, but elsewhere the Red Devils have been plagued by problems.
Jonny Evans is recovering from an ankle operation he underwent in the summer, Chris Smalling will miss a further three months and Phil Jones picked up a back injury while the club was on tour in Norway.
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"Evans is recovering from an operation; Smalling is out for three months," Sir Alex told the club's official website. "Jones got a muscle injury in his back and was sent home from Norway.
"So the area we're concerned about is centre-back. Evans won't be ready for the start of the season. He won't be far away but he won't be ready.
"Smalling is out and I can't give you an update with Jones because we've not fully diagnosed that. But Michael Carrick was absolutely brilliant [in Sweden] with his passing the ball and his interceptions. He was fantastic."