The Turkey international is hoping to come back and haunt his former side after an inauspicious season with the Spanish champions
The midfielder left los Blancos in the summer after an unsuccessful season with the club where he never managed to score at home, but he hopes he can finally find the net at the famous stadium for Fatih Terim's team on Wednesday.
"My goal is to score every game. My only goal when I was with Madrid was against Sevilla and it was in their stadium. I would love to get my first goal at the Bernabeu, especially in the Galatasaray shirt," he told AS.
The Istanbul outfit are underdogs heading into the last-eight encounter, but Hamit believes the lack of pressure on his side could prove beneficial against Jose Mourinho's men.
"This idea helps to motivate the team and take pressure off," he continued. "But our main goal is to get past the quarter-finals.
"Although Madrid are the favourites, these games are a good opportunity for us. But by no means do we feel under pressure."
Many have predicted that Galatasaray will sit back and defend against the Liga champions, but the 30-year-old insists they will be more adventurous than some might think.
He added: "We are a team that has courage. And we also have a coach who wants to be brave. Let's play with the desire and the belief that we can win."