Los Blancos' 2-1 victory over Barcelona has moved them seven points clear of their title rivals with just four rounds of the season remaining, while on Wednesday night Jose Mourinho's men will attempt to overturn a 2-1 deficit in the second leg of their European semi-final tie with Bayern Munich.
After defeating the much-vaunted Blaugrana in their own backyard, Ozil freely admits that he is now dreaming of a double.
"We are very happy," the Germany international told reporters after the win at Camp Nou. "We played well in a very complicated game.
"But we have a very important game against Bayern Munich next week and we'll have to do our best to reach the final.
"Then we'll have to play four more games in La Liga and we'll have to try to win them in order to have a chance to take two titles this year."
Meanwhile, Ozil's international team-mate Sami Khedira, who opened the scoring in Catalunya in what was his 50th appearance for Madrid, admitted that the players are now brimming with belief ahead of the visit of Bayern.
"I'm happy because I scored an historic goal, but the victory is what really counts," the midfielder pointed out. "I think the entire team did a good job and we must keep it up to the end.
"It is very important for the team to win at Camp Nou and today is a perfect day for us. We gave a serious performance for 90 minutes. We worked hard and covered a lot of ground.
"Our match against Bayern Munich will be another final, but we'll do our best to win and reach the final. This victory over Barcelona makes us confident."
Madrid's meeting with the Bavarians in the Spanish capital kicks off at 20.45CET.
Starting last month and continuing for 10 weeks, Goal.com is publishing exclusive extracts from Luca Caioli's new book, Ronaldo: The Obsession for Perfection. The fifth extract, published on Friday, looks at the Portuguese's intense rivalry with Barcelona's Lionel Messi ahead of this weekend's Clasico clash. Don't miss it!