The Gunners midfielder powered home two free-kicks to help his side beat Real in last season's Champions League quarter-final tie and revealed that the goals impressed the former England captain and Los Blancos player - who was known for his dead-ball prowess.
Rice told The Sun newspaper: "He messaged me on Instagram about it.
"That was crazy, because he had some of the biggest moments ever with free-kicks
"I remember the first time I met Beckham was in Qatar. We all approached him. Every player was like, he was a god, you know, because it’s Becks."
Rice has established himself as one of the top midfielders in world football since joining Arsenal in a £105 million move from West Ham in 2023 but confessed that he didn't always think that he would make it to the highest level.
The England international said: "I’ll be totally honest – no, not at all.
"I always believed in myself. I always knew I had ability. What set me apart from others was I had the heart, the desire to go with it.
"I was a really good listener. Even if one of my coaches told me off, I wouldn’t go home complaining to my mum and dad about it. I’d take it on the chin, see where I could improve.
"I didn’t know I would be going on to do what I’m doing. That’s why it’s amazing, because once you start out in football, you never know your journey.
"But if you can stay consistent, believe in your own pathway and believe in yourself, it can take you anywhere."
He added: "It’s something my dad always said to me: ‘How are you going to improve every year? How are you going to get better?’
"It’s taken me to this position and I still can get a lot better than where I currently am."