Giggs departed for a holiday on Tuesday night but is keen to remain at the club he joined 28 years ago if he can continue the role he occupied as assistant to both David Moyes and Louis van Gaal.
So far, such an offer has not arrived. United officials insist he has been assured his future is at the club, but the mystery about what the job might be has left the Giggs camp concerned.
If Mourinho hires regular No 2 Rui Faria, and Giggs is demoted, the 42-year-old might find it difficult to swallow his pride and stick around.
Giggs is already said to be bitterly disappointed United have, in his view, reneged on an agreement to make him manager after Van Gaal.
The discussions he is set to have with Mourinho will be crucial, given the message it could send to club supporters if their idol is seen to have been humiliated and driven away from Old Trafford.
Original source: Giggs looking for a senior role to stay