Madrid play Ajax on Wednesday in the first leg of the last 16, hoping to take one step closer to their fifth European triumph in six years.
Bayern Munich and Ajax have both won the European Cup three times in a row but only Madrid have managed more, when they lifted five on the bounce in the 1950s.
“I believe it’s possible to win four,” Courtois said at a press conference at the Johan Cruyff Arena.
“Every year, if you ask people who are the favourites to win the Champions League, I think they say Real Madrid. We have a really good team, with experience, and we have to show it by beating Ajax.”
Ajax might have felt optimistic when they drew an out-of-sorts Madrid back in December but Santiago Solari’s side have found their rhythm since, winning six out of their last seven matches.
“I feel now they might be more afraid than before,” Courtois said.
“We are ready to fight for everything, to get to the final of the Copa del Rey and go as far as possible in the Champions League.”
While Madrid have found momentum in recent weeks, Ajax appear to have lost theirs. The Dutch side have tasted defeat in two out of their last three games, including a 6-2 thumping away to rivals Feyenoord.
But the talented Frenkie de Jong has been declared fit to face Real in Amsterdam and the 21-year-old will be keen to impress, ahead of his 75-million-euro move to Barcelona in the summer.
“Frenkie is fit,” Ajax coach Erik ten Hag said earlier on Tuesday.
“I can’t deny that playing Madrid will motivate him more. We are all extremely motivated. We are playing the winner of the last three Champions Leagues.”