The England international has been largely out-of-favour since Mourinho took over the reins at Old Trafford from ex-Barcelona manager Louis van Gaal in May 2016.
Shaw recovered from a double leg fracture ahead of the start of the 2016-17 season but the 22-year-old defender has failed to convince Mourinho of his qualities.
He earned a reputation as one of England’s most exciting players after Shaw impressed during his latter teenage years at Southampton before a £27m move to Manchester United in 2015.
Shaw started nine Premier League in the 2016-17 season to struggle to get in the team ahead of his left-back rivals Daley Blind, Matteo Darmian and Ashley Young.
Mourinho handed Shaw a rare start in Manchester United’s 2-1 win over CSKA Moscow in the Champions League on Tuesday night as the Red Devils secured their place in the knockout stage draw.
Former Manchester United midfielder Scholes believes Shaw should be starting in the Red Devils team.
“For me, he has to play. He’s the best left-back at the club, there’s no doubt about it,” Scholes told BT Sport.
“I don’t think he’ll play on Sunday having been out for so long. But we’ve seen what he brings, he turns defence into attack so quickly and he’s a flying machine really.
“We see the quality that he’s got, he’s so strong and powerful. I think if he plays games.
“I can’t think of a left-back like that who can change the pace of the game as quick as he does.”
Manchester United finished in sixth place in the Premier League table last season in Mourinho’s first campaign in charge.
The Red Devils won the Europa League and the League Cup under the Portuguese coach.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news