The Northern Irishman, 32, is an ambitious coach and has been earmarked for a promotion this summer as Mourinho looks to reshape his staff after Faria's surprise departure.
Chelsea warmed-up for Saturday's Wembley showdown with Manchester United by a crushing 3-0 final-day defeat on Tyneside.
Mourinho has already admitted that he has no plans to directly replace Faria and could instead took to re-shuffle his coaching staff, allowing for Michael Carrick to join the team, leaving United without a recognised number two for the immediate future.
Carrick made his final United appearance in the 1-0 win over Watford on Sunday, bringing to an end a 19-year playing career that included 12 seasons at Old Trafford. The end game, maybe, if I get into it and I think I'd like to manage - probably at this stage, my answer would be yes.
'I am going to simply attempt to converse to as many individuals as I can; be a nuisance, be a pest.
"The one under Van Gaal, I wasn't playing, so that was OK - not OK, but reasonable", the 26-year-old said. "We are looking forward to adding a happy ending to the season!"
'I don't want to be throwing quotes out there saying I want to be a manager'.
Mourinho has criticised Shaw's mentality on a couple of occasions over the past two years, but the boss has now reportedly found the Englishman's replacement. I've got other things to do. This was the final chance to cut the cloth clean.
Manchester United ended their league campaign in second spot with an 81-point tally and they now have the chance to contest for silverware this weekend.
Sandro has mostly featured in the left-wing position under Max Allegri this season and his tendency to overlap his wide players is surely an attribute which will have impressed manager Jose Mourinho. "You know why now", Mourinho said.
"There's not a game where you think, "It could have gone either way", I think we've deserved to win the games".