Injuries have put Rio Ferdinand, Jonny Evans, Chris Smalling and Phil Jones all out of action for the start of the Red Devils' season, with Nemanja Vidic partnered by midfielder Michael Carrick at centre-back in the 1-0 defeat to Everton on Monday.
And the Scottish boss conceded that the pair are likely to be needed again, along with winger Antonio Valencia at right-back, for the visit of Fulham on Saturday.
"I don't think any of them [the injured defenders] will be fit for Saturday," Sir Alex told MUTV.
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"Hopefully Jonny Evans is getting near. Obvoiusly we've got a good week's training now and that will bring him on a good bit.
"Hopefully in a couple of weeks we should be okay.
"Michael Carrick's not used to playing as a centre-back but he did all right, he did fine. He applied himself well [against Everton] - they all did."
Having lost their opening game of the Premier League season, last year's runners-up must now look to open their account against the Cottagers, who put five goals past Norwich City on Saturday.