The Reds' boss revealed that the club have been in negoiations for Hargreaves' services for the past few weeks. And, according to the boss, the club are closing in on an agreement.
"You can never be confident but we are hopeful," revealed Sir Alex at his pre-match press conference. "We have been trying to negotiate with Bayern Munich for quite a while now, but it's hit a bit of a deadlock.
"Nevertheless, the boy has said he would like to join United and we would like to have him here.
"We are dealing with a big club in Bayern Munich, but the relationship between the two clubs has always been good.
"We were very amenable to them when they wanted to talk to Ruud van Nistelrooy; we actually would have preferred Ruud to join them [instead of Real Madrid] because that may have helped us with the Hargreaves situation.
"That wasn't to be, but hopefully we can get something done. It's in David Gill's capable hands. He's doing his best."
Sir Alex highlighted the England international's maturity in the holding midfield position as one of the main reasons behind United's interest.
"We've always known about Owen," declared the boss. "At 25, he's at a good age to come to a big club like United and he would fit in with the structure of our football club in terms of age.
"He's played against us a couple of times over the years. In one match he was out on the right wing, and in the next one he played at right-back.
"So he's played in a variety of positions but he's now got a settled position which he enjoys. You can see how he's matured into that role and his performances for England at the World Cup emphasised that.
"I wasn't surprised by how he played for England the other night against Greece because we know he's got that quality."