Madrid will travel to Manchester on Friday for the second leg of their Champions League last 16 tie, which is delicately poised after a thrilling reverse fixture at Santiago Bernabeu.
Zinedine Zidane's men took the lead through Isco, only for late Gabriel Jesus and Kevin De Bruyne goals to give City a famous 2-1 victory in the Spanish capital.
Real have since bounced back from that disappointment to win their first La Liga title since 2017, while Pep Guardiola's men were dethroned by Liverpool in comprehensive fashion in the Premier League.
Zidane has never lost a European knockout tie on aggregate as Madrid head coach, and Varane says the entire squad are motivated to keep that run going at Etihad Stadium.
"We want to win every day, we're Real Madrid," the France international said in a video message posted on the club's social media accounts. "We want to win everything possible and gain more confidence that way.
"We haven't had games to play beforehand, so we have time to prepare ourselves. The best team on the day will win. We'll go into [the game] with hunger to win and the necessary determination."
Varane added on the likelihood of another fiercely competitive contest between two elite teams: "[It will be] a difficult game against a very good team. The first leg was a top-quality game, with pressing from both teams. "It was decided by the small details.
"[Real Madrid and City are] two teams that like to have the ball, are very intense and that require lots of concentration.
"These are the best games in the Champions League - the ones that are decided by very little. They are why we love this competition."
Madrid won three European Cups in a row during Zidane's first spell in charge, and Varane says that experience holds them in good stead to avoid an early exit this time around.
"We know what we've achieved in recent years is something exceptional," he continued. "What we have to do is carry this experience with us and know that the small details make the difference in big games.
"Now, we're a bit more relaxed, but we have the same determination and we know the traps we have to avoid. We have years of experience, but it's hard to win every game, repeat victories and always be at the top."