Bendtner has scored 15 goals for the Gunner this season.
He told Ekstra Bladet: “It is of course a priority of mine to prolong my contract, and I have never said anything else.
“For me it is of course sweet to receive the backing from the manager, and I hope to stay at the club for a long time.”
The 21-year-old joined Arsenal from Danish side FC Copenhagen in 2004.
Bendtner’s current contract is set to expire in 2012.