Arsenal head to Wembley on Sunday looking to win their first trophy since they beat Manchester United on penalties to lift the 2005 FA Cup.
Manager Arsene Wenger will hope Van Persie is fit to lead the line given that he's scored five times in his last three matches.
Wenger left the Dutch striker out of the 1-1 draw against Leyton Orient in the FA Cup and revealed the 27-year-old, and Koscielny, would be absent at the Emirates on Wednesday.
"We do not have Van Persie available or Koscielny and (Thomas) Vermaelen has a long-term (Achilles) injury,'' Wenger told Arsenal TV.
"Van Persie has a hamstring problem and Koscielny has a back problem but they both have a chance to be involved on Sunday.''
"Johan Djourou missed out on Sunday but he is better and will play tomorrow,'' Wenger added.
Wenger's side beat Barcelona at the Emirates Stadium last week but were brought swiftly down to earth against League One side Orient on Sunday.
Nevertheless, the Gunners know that a return to winning ways against Stoke will see them close the gap on leaders Manchester United to just one point in the first match in a gruelling schedule which could see them play six times in 17 days.
Arsenal have lost three times at home this year - more than any other team in the top six - and Wenger thinks their form at the Emirates could prove decisive in their push to win their first title in seven years.
"We know we are in a strong position,'' the 61-year-old said. "The players know that at home our results will have a vital importance to have a chance to win the title.
"The focus will be natural, this team wants to win every single game and the players are disappointed after the Leyton Orient result.''
Wednesday's game will see the renewal of a rivalry which has boiled over on several occasions over the last few years.
Stoke manager Tony Pulis accused Wenger of "moaning like a drain'' over fixture congestion last season, while the Frenchman slammed Stoke defender Ryan Shawcross for his "horrendous'' tackle which broke Aaron Ramsey's leg in March 2010.
"What is important for us against Stoke is for us to have the ball, because the more we can have the ball then the less dangerous they can be in the air,'' he said.
"We will try to dominate and master the game, because as long as we have the ball, they cannot be dangerous.''