The Italian midfielder signed from London rivals Chelsea last January for a fee of £12m.
There have been rumours of potential exits for Granit Xhaka and Thomas Partey.
Since his arrival in January, Jorginho has established himself as an integral squad member for the Emirates-based outfit.
The Gunners have returned to the Champions League and Jorginho is one of the few players in the squad who has experience in the competition.
However, Arsenal are in the process of signing West Ham captain Declan Rice in a bid totalling £105m.
“I’m very happy to stay at Arsenal, to be honest,” Jorginho said.
“Those rumours, I’m not sure who was behind it, to be honest, but nothing at the moment has happened to me. I’m quite happy where I am.
“I hope we can do even better next year. It’s been a while [since Arsenal have been in the Champions League]. Everyone is very excited. Everyone can’t wait to play with the ball with the stars. It’s going to be an exciting season for sure.”
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