The Turkey international insists he bears no grudge towards the Blancos despite his unfruitful stay last season, while urging his side to take their chances on home soil
The 30-year-old joined the Blancos on a Bosman deal in the summer of 2011 from Bayern Munich, but mustered only 12 appearances in all competitions before opting to cut his spell short in favour of the Super Lig holders.
Nonetheless, Altintop insists he bears no ill-feeling towards Madrid and is hugely grateful to have represented the club in his career, while speaking of his admiration for then-coach Jose Mourinho and ex-colleague Cristiano Ronaldo.
"I have no hard feelings towards [Real] Madrid or anything of the sort. I have only good words for the club. I'm a person who always thinks positively and very few players in the world can say they've played for them," he told Marca.
"Mourinho is a great coach and person who knows a lot about football and has everything under control. He handles things in the dressing room effortlessly. He knows when to be close with a player and when to walk away.
"[Ronaldo] is a decisive player and one of the best in the world, but Madrid are not just about Cristiano, they are a great team. If we thought we could progress only by stopping Cristiano, we'd be wrong."
Hamit then highlighted the importance of stifling his former side in the opening match at Santiago Bernabeu and taking their chances in the return fixture, but only if his Galatasaray team-mates believe in themselves.
"I'm very happy here [at Galatasaray]. The club came in for me and I don't regret the decision I made," the midfielder added.
"In football, anything is possible. I have played in many matches where I've won despite being considered an underdog. The key will be, if we can hold out, taking our chances on home soil."