"The Premier League is hard, and I have come with an injury - clubs do not normally take such risks," he said.
"But Arsenal have shown faith in me and are building me up with a daily [fitness] programme.
"I know about the competition for places here - nobody can take their place for granted, but I am working hard and there is no reason why it should not work out for me."
Bischoff was born in France, from the same Alsace region as Wenger, but decided to play for Portugal, being eligible though his mother.
The 21-year-old is determined to fit right in with the Gunners' quick, passing game.
"It is a style I have admired for many seasons.
"Arsenal play the most beautiful football in Europe. It is the best to watch on TV and for the fans as well. That is why I have come to such a great club."