Sky Sports is reporting that the incoming Portuguese is eager to have Giggs stay at Old Trafford but wants to find another role for him.
There has been plenty of talk that Giggs will follow departed manager Louis van Gaal out the exit door and Mourinho wants to avoid that scenario.
The former Chelsea boss will have long-time assistant Rui Faria at his side, meaning Giggs will likely take a step down, which may not suit the Welsh great who is eyeing a career in management.
Mourinho is well aware of Giggs' standing at United and is looking to create a role that will see his 29-year association with the Red Devils continue.
Additionally, The Sun suggests Giggs will be offered the U21 job currently held by Warren Joyce who has been approached by Blackburn Rovers to take their first-team role.