Van Persie is expected to lead the Manchester United attack against his old club and Koscielny is ready for the challenge as the Gunners go in search of a 10th win in 13 Premier League matches.
The Frenchman said: "I hope we can keep Robin quiet. He is a good player. I enjoyed my time playing with him, but I hope we keep the story with us.
"It will be a hard game for the whole team, but we are at home and we will try to get the three points. It will be a good game against a big team."
Koscielny is likely to line up alongside Per Mertesacker, who scored the winner in Saturday's victory at Fulham, and he is enjoying his partnership with the German.
He said: "We play well together as a pair. We communicate on the pitch well.
"His experience is vital and it helps us work together on the pitch, so we try and talk to each other a lot and it is important at the back to have an understanding."
Koscielny added: "Per is a very good player. He reads the ball well. He is clever, attacks the ball and wins headers whereas I can go behind and be quick and cope with the long balls.
"He is good technically so he is good for the defence. Per is calm on the pitch.
"He is good for me, he uses his experience, this helps me, and he helps the team."