He told the BBC Radio 5 Live interviewer "I'll be here next season, yes. It will be okay."
Asked if he had been offered a one-year extension to his current contract, Bergkamp replied: "For one year, yes".
Meanwhile Robert Pires has yet to agree terms with the club on an extension to his current deal which expires in the summer of 2006.
He said today:
"I have one more year left on my contract, but there has been contact from other clubs. I gave my position to Arsenal. I would like to sign for two or three years, but it is not for me to decide but Arsene Wenger and David Dein. They will let me know after the cup final.
"You never know in football why they are reluctant and you never know what could happen. Maybe the manager is not the only one who decides. At the moment the offer is for one more year to 2007."