Although his team have begun the Turkish championship with three draws and one win from four games, the former Chelsea player is convinced Galatasaray can upset Gareth Bale, Cristiano Ronaldo and company.
"It's a new season and we know we can beat them again," Drogba told a news conference on Monday.
"The best thing to do is play good football and give 100 percent to win. Once again we are going to face the top clubs of Europe this season and I think we have a good chance to qualify (for the knockout stages)."
Galatasaray went out 5-3 on aggregate despite beating Real 3-2 in their quarter-final second leg in Istanbul five months ago.
"No team comes to Istanbul comfortably. We believe we can challenge any team," said coach Fatih Terim.
Real, seeking their 10th European crown, signed Bale for a world record fee earlier this month and it will be tough for Galatasaray to keep the Wales winger and dynamic Portugal forward Ronaldo quiet.
"The Real Madrid team consist of stars of incredible quality in every position. They have made important transfers but they had one of the best teams in the world anyway," Terim said.
Terim, now in his third spell at the club, was behind Galatasaray's 2000 UEFA Cup title triumph and led Turkey to the semi-finals of Euro 2008.
He has taken on an extra burden this season, assuming a temporary role as coach of the national team in their uphill battle to qualify for next year's World Cup.