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Goals from Gabriel Jesus and Kevin De Bruyne have put Pep Guardiola's side in the ascendancy ahead of their Etihad Stadium reunion on Friday.
With huge financial backing, City have been competing in European football's elite competition each season since the 2011-12 campaign, reaching the semi-finals in 2015-16 when Madrid edged them out 1-0 over two legs.
Toure told Stats Perform News: "City have to win the Champions League. They've been so unlucky for so many years, but I pray for them to do it. When I joined that was my dream, to win the Champions League."
He sees Guardiola's leadership as the key to ongoing success for City, who were overhauled by Liverpool in the Premier League but have real hope of becoming European champions this month.
"They have a top manager, they have to keep him there and make sure they bring players who can add value," Toure said. "They need players who have experience of winning the Champions League. They have a big chance against Real Madrid."
Pointing to last season's Champions League exit, when a dramatic quarter-final saw City edged out by Tottenham on away goals, Toure reflected on how a little good fortune can go a long way.
"You need a bit of luck, they were so unlucky againstTottenham," Toure said. "I hope that they will win."
The arrival of Nathan Ake from Bournemouth for next season has raised questions about Stones' future at City.
"He needs to be consistent. He lacks it," Toure said. "He's a really good player with many qualities but needs to work on his concentration. Sometimes he does things that you don't know where they come from, because he has everything.