The manager says the club would like to sign the Brazilian but insists no agreement has been reached just yet and insists the club is trying to bring in new players.
It is believed that United has already seen one bid in excess of 20 million euros turned down by the Brazilian giant but is expected to return with an improved offer of 32m euros.
The 19-year-old attacking midfielder has been the subject of intense transfer speculation throughout the summer but Sir Alex has now has admitted to concrete interest in the youngster.
The Scot was keen to stress, however, that it was just interest at this stage, insisting that no agreement had been reached over the transfer.
“We haven’t reached an agreement. We’ve shown interest," he told reporters. "Until such time we reach an agreement, we can’t say he [Moura] is ours."
The 70-year-old also stressed the club is working hard to bring in other targets to add to the captures of Shinji Kagawa and Nick Powell.
"We've signed two players in the summer. Kagawa and Powell," he continued. "We think they both have fantastic potential. We’re not lying on our backsides doing nothing.