The Netherlands international has scored just twice for United in 2014-15, putting him under pressure to retain his place in the team.
United captain Wayne Rooney returns from a three-game suspension for the Manchester derby, meaning that Sunday's clash against Chelsea could be Van Persie's last chance to keep hold of his starting spot, but Van Gaal expects the 31-year-old to get back to scoring ways.
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"So a striker needs also a bit of luck and then the confidence is higher but he's self-confident so I expect he shall score and maybe against Chelsea."
Despite being under an injury cloud, Van Persie scored four goals at the World Cup this summer as the Dutch, coached by Van Gaal, finished third and his boss says that he is now in better shape than that.
"I think he is more fit than ever," Van Gaal continued. "He doesn't score so much. In the Dutch team he has scored more than now for Manchester United and then he was not so fit as now.
"That's remarkable but he scored in [almost] every game for me in the World Cup in spite of maybe his 80 per cent fitness. He scored four goals out of six games and then also a penalty so maybe now he is playing better but doesn't score as much.
"Every striker has to be at the attacking point. He has to play with the other 10 players. That is also important. That he is now doing better than in Dutch team."