The Belgium international was linked with a 5.5million euros move to the Premier League club but Dembele was sceptical when asked about the speculation.
"At first I thought: Arsenal, that's nice," he told the Het Nieuwsblad newspaper. "But when I heard the amount, I reacted totally differently. I moved for 5.5 million from Willem II to AZ. So it was just a joke.
"If an interesting offer comes, I'll consider it.
"For this reason it doesn't have to be Manchester United or another big name."
"Why should I leave if we can maybe play the Champions League very soon?" he said.
"There's a chance that I will stay in Alkmaar."