Courtois joined Los Blancos from Chelsea this summer, shortly after Zinedine Zidane had led them to the biggest prize in club football for the third year in a row, and a fourth time in five years.
Madrid have since lost Zidane and star player Cristiano Ronaldo, but Courtois is still confident that they have the quality to challenge in Europe once again, having been on the losing side against them with Atletico Madrid in the 2014 final.
Speaking after being named the Goalkeeper of the Year at FIFA's The Best awards, Courtois told Sports Mole: "[I am] very happy, very proud.
"Obviously I think it's a nice trophy that you can win - an individual award, obviously the team awards are more important, like winning a league, winning a European Cup, that's always the best but getting recognition for your season is always nice.
"Obviously I missed out once against them [in the Champions League final] four years ago, so I hope maybe this season or in the future to win it. I think we have a great team and we'll do our best to win another title."
No team has won four consecutive European Cups since Madrid themselves won the first five editions of the tournament between 1956 and 1960.