The 27-year-old defender had been linked with a move away from north London, after losing his place in Arsene Wenger's first-team, following a recent slump in form.
However, after reclaiming his place in the Gunners side, starting the past two games at centre-back ahead of captain Thomas Vermaelen, Koscielny has moved to distance himself from rumours he was ever unhappy at the club.
"My contract lasts for another four years," the France international is quoted as saying in The Sun. "I have no wish to be elsewhere."
With Koscielny currently away on national team duty, the Arsenal stopper welcomed the inclusion of Real Madrid's rapidly emerging talent, Raphael Varane, even though it will increase competition for places in Les Bleus side.
"Do I feel threatened by Raphael Varane? No, it's good competition," he added. "This will push me to be even better and drive forward with my club Arsenal."
Per Mertesacker is currently Wenger's first-choice partner for Koscielny at the heart of Arsenal's defence, after Vermaelen suffered a similar dip in form over the past few weeks.