A £112million fee with Juventus and a £275,000-a-week contract have already agreed for the Frenchman.
And Mourinho is now turning his attention to bringing another centre-back to Old Trafford.
ESPN claim the Portuguese boss wants a defensive leader in the style of former United captain Vidic.
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United have apparently discussed the possibility of bringing in Southampton's Jose Fonte.
While they are also interested in signing Leonardo Bonucci from Juventus, but face competition from Manchester City.
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ESPN add United are monitoring Everton's John Stones, with the Toffees willing to sell the England international for £50m.
United have already signed one centre-back this summer.
Eric Bailly has joined for £30m from Villarreal, but he is not an experienced leader in the style of Vidic, and Mourinho wants reinforcements.