Having arrived from Ukrainian side Shakhtar Donetsk, Fred is yet to enjoy more playing time, though has been featuring for the side in several big games.
Spending just a year at the Old Trafford, the 26-year-old has been linked with a move to Serie A outfit Fiorentina, but Solskjaer has reported the former Porto Alegre man is nowhere near an exit from Manchester United as he hints of a chance for him in the new season.
“He [Fred] is working hard and at the moment he's just behind Paul [Pogba] and Scott [McTominay] – who has done really well – and Nemanja [Matic], who hasn't been involved," he told reporters.
"August is the most difficult period to manage a big squad because there's only one game a week and everybody's fit because we've had pre-season, and everyone's ready to play.
"In September, October, November – when injuries come – that's when you have most of the games.
"So, he [Fred] will play plenty of football."
Fred, in last season, scored one goal with one assist in seventeen Premier League appearances for Manchester United, but recorded no goal in his six Champions League games.
After reporting late from a long honeymoon vacation, Fred is yet to feature in Solskjaer’s match-day squad with the side having already played three games with one win, one defeat and a draw.
Manchester United is set to be hosted by Southampton at the St Mary’s Stadium on Saturday for their fourth game of the season.
And having lost to Crystal Palace at Old Trafford last week, United will look to win the maximum points as Southampton also expect to extend their winning streak after defeating Brighton Hove Albion away from home.