The Brazil midfielder has failed to justify his £18m price tag since arriving from Porto in the summer of 2007 with the intention of one day replacing Paul Scholes in the side.
But it has not gone to plan for the 21-year-old so far amid reports of a bust-up - which has been denied - with boss Sir Alex Ferguson.
Solskjaer has seen Anderson up close for the second string and feels there is plenty more to come from him in the future.
He told the MEN: "Ando has shown his qualities and attitude. 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. "