The Internacional playmaker was part of the Chile side that impressed at the 2014 World Cup, and he has subsequently been linked with a move to some of Europe's biggest clubs.
The Mirror claims that Arsenal are monitoring the player, but no contact has yet been made.
Aranguiz told reporters: "I don't know anything about it. I've heard about it through the press but nobody has talked to me. They're a great team, and it would be a dream, but for now that's all it is...a dream."
The 25-year-old started for Chile in their defeat to Brazil at the Emirates Stadium yesterday.