The Brazilian has been under-fire following several average performances for United.
Anderson have lost his plas in Sir Alex Ferguson’s starting XI at Old Trafford.
“Ando has shown his qualities and attitude,” Solskjaer 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.”
Solskjaer added: “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.’
“It is always going to be a big challenge at United to get a place in the first team.
“No player at United is going to step aside and say ‘here you take my place.’
“You have to fight for it and he is more than capable of doing that as he is proving.”
