The showpiece in Lisbon on May 24 will be the first time in the competition's 59-year history that two teams from the same city compete and is los Merengues' first final since a 2-1 win over Bayer Leverkusen in 2002.
The retired full-back, who won the European Cup with AC Milan in 2007, acknowledged that the clash was likely to be tight but felt that Madrid, with Ballon d'Or winner Ronaldo in their ranks, were the most likely winners.
"I think Real Madrid will be champions," the 43-year-old told ESPN Brasil.
"Even though Atletico are one of the best European teams at the moment, with it being a single match, something that Madrid is used to playing, with athletes that used to the competition, a team that has already won it nine times, I think it will be Real.
"And having the best player in the world [Cristiano Ronaldo] also helps. It's always a positive reference for the team. You can give him the ball all the time. If you have the best player in the world, in a fantastic phase, it will only weight more towards Real."
Cafu also took the time to reflect on his own experiences in the competition, including Milan's 2005 defeat to Liverpool, which he described as "the greatest shock of [his career]" after losing on penalties despite leading 3-0 at half time.
"We weren't being arrogant, but I'd be lying if I said we didn't have a feeling that it was very close," he said.
"It was a Champions League final, against Liverpool, we were winning 3-0 at half time, obviously you get more relaxed for the second half.
"But we got a scare, because they scored the first too quickly. And then the second one was even quicker. When we finally came to our senses it was already 3-3.
"That was the greatest shock of my career. Especially because of the team we had. That Milan team should've never lost anything, no way.
"Two years later, another final, Liverpool again, we scored first and I thought, 'Damn, we can't let this slip this time'. And we made it and conquered the Champions League, at last."