There has been no official reason given as to why the Serbian has not been included, but he has struggled with a knee problem in recent months and rarely played back-to-back matches last season.
For a similar reason, Javier Hernandez will not take part at all and will instead train at Carrington once his holiday period has concluded.
Man United's pre-season squad:
Goalkeepers: Anders Lindegaard, Ben Amos
Defenders: Rafael, Phil Jones, Rio Ferdinand, Jonny Evans, Patrice Evra, Alex Buttner, Fabio, Michael Keane
Midfielders: Michael Carrick, Anderson, Tom Cleverley, Ryan Giggs, Wilfried Zaha, Jesse Lingard, Adnan Januzaj
Strikers: Wayne Rooney, Danny Welbeck