As exclusively revealed by Goal.com, United have already seen one bid in excess of £20 million turned down by the Brazilian giants but are expected to return with an improved offer of £32m.
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.
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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 their 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.
"We’re trying hard to bring other players to the club.”
The Premier League runners-up have also been linked with a move for Real Madrid's Nuri Sahin, as revealed by Goal.com, should they become frustrated in their attempts to sign Lucas.