Diallo is part of the United travelling squad to take on Granada in the first leg of the Europa League quarter-final tie away from home at Estadio Municipal Nuevo Los Carmenes on Thursday evening.
The 18-year-old former Atalanta winger scored against AC Milan in the first leg of their Round of 16 tie at Old Trafford last month.
The teenager officially joined United from Atalanta in the January transfer window and has been playing mainly for the Under-23 side so far.
The Ivory Coast international has made three substitute appearances in the Europa League for United and has yet to make his debut in the Premier League.
When asked if Diallo is any closer to making his first start for United, Solskjaer told the club’s official website: “Yeah, of course he is. He’s getting more and more used to our expectations and standards, the training, the level of intensity in the games over here.
“He did well when he played 45 minutes against Milan, definitely a bright start and we’re gradually going to see him play more and more and a start might come now, it might come in a little while.”