The 58-year-old will take charge of the Serie A side and the end of this season and the former Tottenham Hotspur and Manchester United manager is already looking to raid both club for a few of their players.
According to Corriere dello Sport, Mourinho is not expected to sign high-profile players this summer and he is looking to strengthen his midfield options, identifying Hojbjerg, Dier and Mata as three realistic targets for Roma to enquire about.
Hojbjerg, who Mourinho signed for Spurs in August for around £15m, has made 34 appearance this season but the North London club are unlikely to entertain parting ways with the midfielder.
Dier also featured heavily under the Portuguese boss at Tottenham, playing 33 times in all competitions, and the former Sporting Lisbon defender may be tempted to move abroad once again if he decides to look for a new challenge elsewhere.
Meanwhile, Mata will see his contract expire at the end of next month and although the Red Devils are considering offering the Spaniard a new deal, the 32-year-old may feel that a reunion with Mourinho - who he played under at Chelsea and United - and a switch to Serie A could be a good move for him at this stage of his career.