Carrick is due to retire at the end of this season, after which he will join Mourinho's backroom staff as a coach.
One of United's transfer priorities will be replacing Carrick, particularly due to the ongoing uncertainty over the future of Marouane Fellaini, and Metro reports that the 36-year-old has been asked to cast his eye over potential recruits.
Manchester City are currently considered favourites to sign Jorginho, leading to United prioritising moves for Milinkovic-Savic and Fred, although they are still keeping track of the Napoli midfielder should their local rivals drop their interest.
Mourinho has reportedly entrusted Carrick to run the rule over the trio and will consider his opinion when it comes to making the final decision over which player to pursue.
Carrick has been at Old Trafford for the last 12 years, making 463 appearances and scoring 24 goals.