The former winger was assistant to Louis Van Gaal and while it's reported he has been offered a role under Mourinho it's uncertain which one.
Scholes says Giggs has a lot to offer.
In other manager news, it seems Rafa Benitez will stay on as Newcastle manager.
Having arrived late this season Benitez could not save the club from relegation despite improving their form.
It's believed he's agreed a three year deal with the Magpies.
It's reported the former Liverpool and Real Madrid manager will have full control over the clubs transfers dealings.
Meanwhile, Arsenal have finally announced the signing of Swiss international Granit Xhaka.
The highly rated midfielder will join from German side Borussia Monchengladbach for an undisclosed fee.
Pictures of Xhaka in an Arsenal kit emerged on social media at the weekend.
