The 21-year-old has made 42 league appearances for the Red Devils since arriving from Porto in 2007.
But he has struggled to establish himself in Sir Alex Ferguson's starting XI so far this season, with the Brazilian international receiving criticism from fans and media pundits alike for his under-par performances.
While reports have suggested that Anderson and Ferguson have fallen out following the latter's decision to omit the Brazilian international from the Community Shield defeat to Chelsea in August.
However, the midfielder recently played and scored in a United reserve match against Wigan, and Solskjaer - who made 235 league outings for the club, netting the last-gasp winner in the 1999 Champions League final - is confident he can play his way back into Ferguson's first-team plans.
"Ando has shown his qualities and attitude," he told the Manchester Evening News.
"Now it is a case of him taking his chance when he gets it and putting down a marker to stay in the team.
"He is going to be a big player for Manchester United.
"It was all glory for him in the first season, but then you sometimes get a bit of a reaction to that. It happens to a lot of players.
"But with Cristiano Ronaldo gone, we need players like Anderson to step up and say 'here is what all the talk was about when you signed me.'
"You have to fight for it and he is more than capable of doing that as he is proving."
