The Daily Mail is reporting that the Red Devils want to bolster what has been a problem position in the Manchester United team under Jose Mourinho.
The same article states that the Portuguese head coach has run out of patience with England international Luke Shaw.
According to the Daily Mail, Manchester United supporters would welcome the addition of Juventus star Alex Sandro or Celtic prospect Kieran Tierney this summer.
Manchester United have already been active in the summer transfer window following the confirmation of two deals.
The Red Devils are reported to have agreed a £52m deal with Ukrainain Premier League champions Shakhtar Donetesk for Fred.
The Brazil international, who suffered an ankle problem on international duty, is still to complete his transfer due to a hold up with his work permit.
Manchester United have also reported signed Portuguese full-back Diogo Dalot in a £17m deal from FC Porto earlier this month.
The Red Devils finished in second place in the Premier League table last term to ensure their continued participation in the Champions League next term.
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