The Old Trafford goalkeeper could even get the nod next season, as his manager decides who can be relied upon in his squad when the chips are down.
It may also be a further signal that United are confident the Spain international is ready to commit his long-term future by signing a lucrative new deal in the coming months.
Current first-team skipper Michael Carrick is retiring in the next few weeks, although Mourinho still is not sure yet if De Gea is ready for the armband.
Regardless, the Red Devils' boss feels the brilliant shot-stopper is one of only a handful of players who have been at the club long enough to understand the expectations at the Theatre of Dreams, since his arrival back in 2011 from Atletico Madrid.
De Gea is a quiet individual inside the United dressing room but Mourinho has discussed with his backroom staff whether the 26-year-old can handle more responsibility.
Mourinho refused to name a vice-captain last summer, which is something he could also revisit if he decides De Gea is not quite the right fit for the main job.