Rosler believes Van Persie needs to do better with Holland to earn such a tag.
The Brentford manager told the Manchester Evening News: "It doesn't matter if you are a World Cup player or a League One player, you need to be consistently training to get the best out of you.
"Van Persie has been outstanding for United and before that for Arsenal.
"But for Holland at the big tournaments, he has not really fired and performed to the way that he does in the Premier League.
"And for any player who wants to be known as a world star, you have to do it domestically, in the Champions League but also in the biggest tournaments for your country."