The duo locked horns over the years when they played in the Premier League against each other along with several clashes at international level between England and Portugal.
"Real Madrid will be a huge test for us, they're obviously one of the best teams in the world and I've had some good games with Cristiano Ronaldo down the years, so I hope this will be another exciting match," Cole told the club's official website.
"It will be great to catch up with Carlo Ancelotti, who is a great guy. We loved working with him at Chelsea and hopefully he can have a good first season in Spain."
Chelsea begin their Premier League campaign against Hull City on August 18.