The Santiago Bernabeu side beat Atletico Madrid 4-1 after extra time last season to win their 10th European Cup in history and the former Tottenham Hotspur star is desperate to add more silverware to the club's trophy cabinet in the 2014-15 campaign.
"Winning the club's tenth title was fantastic for everyone. Scoring a goal in the European Cup final is one of my biggest dreams," Bale said at a press conference.
"It was a good season for the team. I felt fulfilled.
"We have to look to the future and try to win it again. We want to make history by winning the Champions League again.
"We know there is always a lot of pressure on us, but we like it and we want to win more titles this year."
Madrid beat Sevilla 2-0 earlier this month to bag the European Supercup, but were beaten to the Supercopa de Espana by Atletico over two legs (2-1).