The Spain international joined Arsene Wenger's side from Malaga in August 2012 and soon became a firm favourite with Arsenal fans.
Cazorla revealed that he held talks with Real over a move to the Bernabeu before he joined the London club and admitted he would have been living the dream if a switch to the Spanish giants had gone through.
The playmaker would also have relished a move to Barca, but believes it was not meant to be.
He told RMC: "Those two clubs are monuments of Spanish football. They make all players dream. I had contact with Madrid a few years ago, but it didn't come off.
"Several times, destiny has meant that I haven't been able to join one of those two clubs. But my career has just happened like that, and I don't regret anything."
Cazorla will be aiming to inspire Arsenal to a victory over Manchester United on Wednesday that would move them back to the top of the Premier League.
