Diallo completed his move from Atalanta earlier this month in an initial £19m deal, which could rise to £37m with add-ons.
The 18-year-old winger has only made five senior career appearances since making his Serie A debut last season but could feature for United sooner rather than later.
When asked about how Diallo had settled in, Solskjaer said: "Very good. He can handle the ball, he's enjoyed training, he can make a difference in training, which is remarkable at his age.
"Some adjustment to settle into the hustle and bustle of the Premier League but I can't see it being too long until he's in the squad.
"It might be quicker than [four to five weeks], who knows? He's definitely settled down well, the players have taken to him. He's a very good character, a polite and smiley boy who works hard.
"He's doing his session, getting used to us, there's always a period of adjustment needed but he's settled in well."
Diallo scored one goal in his five senior appearances for Atalanta - on his debut in October 2019 against Udinese - before signing a contract until 2025 at United, with the option of another year.
Upon his arrival, Solskjaer said that Diallo is “a player with all of the raw attributes that are needed to be an important player for Manchester United in the years to come”.