Shaw has impressed for United in the early stages of the campaign, but the left-back will see his current deal at Old Trafford expire in June, and it has been reported that the England international is in no rush to extend his contract.
Herrera and Mata will also see their deals expire this summer, and both have been linked with moves away from the 20-time English champions having fallen out of Mourinho's first XI.
The United boss, however, has said that he is desperate to keep hold of the "unique" Spanish duo.
"I hope they (Shaw, Herrera, Mata) will stay. We had a similar conversation last season about Marouane [Fellaini] and I was always saying I hope he stays, I believe he stays," Mourinho told reporters.
"Juan and Ander, even if they are not playing or not playing a lot, not starting matches, by the personality point-of-view and character point-of-view, by what they represent in the modern society in football, they are almost unique pieces that I also don't want to lose."
Shaw and Herrera are both doubts for United's trip to Watford in the Premier League on Saturday, but Mata could return to the matchday squad having fallen out of favour in recent weeks.