The Italy international has been linked with a return to Serie A, where Juventus are keen.
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However, Materazzi can see Udogie joining United and eventually replacing Luke Shaw at left-back.
"Is Destiny Udogie the right player to replace Luke Shaw at Manchester United? I think so," he tells Hajper.
Meanwhile, Materazzi is urging Italy star Sandro Tonali to stay with Newcastle United.
He added, "Sandro Tonali can play for any team in Italy and England, but he needs to decide if he wants to stay at Newcastle because they believed in him.
"The city, the fans and the club were behind him. He has to think about that too, not just whether he can play for Arsenal, Liverpool or Manchester United. I hope he stays at Newcastle and builds on his legacy."