Koscielny's future at Arsenal had been the subject of speculation after he lost his place in Arsene Wenger's starting line-up earlier this season.
However, the French stopper has won his place back in the side and has started the last two games in central defence ahead of captain Thomas Vermaelen.
The 27-year-old still has four years to run on his current deal and he insists he is happy to stay at Arsenal.
"My contract lasts for another four years," Koscielny is quoted as saying in The Sun. "I have no wish to be elsewhere."
Koscielny insists Arsenal will fight until the last minute in their bid to qualify for the UEFA Champions League.
"Arsenal will fight until the end to be in the Champions League," added Koscielny. "It will be difficult, but we will give everything."
Koscielny, who is currently away on international duty with France, has welcomed the inclusion of Real Madrid defender Raphael Varane to the squad even though it increases competition for places in Didier Deschamps' squad.
Koscielny does not fear for his place in the side following Varane's call-up and he feels the competition for places will only improve him as a player.
"Do I feel threatened by Raphael Varane? No, it's good competition.
"This will push me to be even better and drive forward with my club Arsenal."