Mourinho will bring his trusted coaches Rui Faria and Silvino Louro to Old Trafford with him but he is still keen to bring in recruits that are knowledgeable of the club.
According to The Mirror, Kidd who made over 200 appearances for the Red Devils, is considering a return to his old club.
But Kidd has worked with Manuel Pellegrini at rivals Manchester City for three years and is concerned about the backlash he would receive from fans.
With Pep Guardiola arriving at the Etihad this summer, it is unclear whether the Spaniard will want to keep him on.
United believe Kidd would help develop the likes of Marcus Rashford and Cameron Borthwick-Jackson into first-team regulars.
Neville struggled in his first spell at management with Valencia, but his knowledge and understanding of the club would be a welcomed addition to Mourinho's reign in Manchester.
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