Giggs has clearly had sights on the manager's job since Moyes was sacked hence him accepting the number two job with a successon plan to become manager in 2017. Now that hasn't happened, and he still wants the job, I don't see why Mourinho would keep him anywhere near the first team because as soon as things go wrong (hopefully not too soon!) the media attention will turn to Giggs as it did towards the end of LVG's reign hence the 'Giggs in managerial mode' joke whenever United were losing and Giggs was on the touchline giving instructions when he rarely ever did when United were winning.
No top elite level manager would really accept a club legend, like Giggs, to join as a number two for the aforementioned reasons above. Giggs' role under the LVG set-up as to assess the opposition and relay that to the players and last season showed Giggs was doing the job well....
There are other candidates around who could join Jose's set up and offer just as, if not more, valuable input than Giggs namely the under-21 coach Warren Joyce, who received plaudits for his work with that age range last season; Rio Ferdinand has been linked and with his personality, might work nicely with the younger players and he wasn't that bad a defender...; or if Gary Neville wants to come back under Mourinho as a coach rather than an assistant - above point returns again but they seem to have got a good friendship which might help.
Giggs would either be better off to accept a different role, work behind the scenes at United (with the younger age ranges perhaps) or leave and become manager elsewhere.