The 34-year-old lifted the trophy with Barcelona in 2009 after a 2-0 win over Manchester United in the final, but he has only gone as far as the last four on one occasion during his eight-year spell with City.
Toure has won two Premier Leagues, two EFL Cups and the FA Cup in England and will go down as one of the finest players in the club's history, while he also claimed the Africa Cup of Nations with Ivory Coast in 2015.
But the former Monaco man admits his legacy will only be complete if he can conquer Europe before bringing his City career to an end.
"I want the Champions League again – so badly," he said, as quoted by The Mirror. "I have won everything in England with City and now I want something that is really special for the fans and the club.
"I have been lucky enough to win some important trophies for my clubs and also Ivory Coast. But the Champions League is special. To be happy, I really need to win it again."
He continued: "To be honest, the Champions League is the most difficult competition in football. It is so hard to predict who will win it because all the teams have great quality.
"You have to be focused for every game because teams like Barcelona, [Real] Madrid and Juventus are excellent teams who are better than the teams we face in England.
"Experience is so important – and we have that now."
City's 3-2 win at West Brom on Saturday means they have made the best start of any team over the first 10 matches in Premier League history, with 28 points claimed and a goal difference of 29.
They have also won three out of three in Champions League Group F and will secure a spot in the last 16 if they avoid defeat against Napoli on Wednesday.
Toure believes City are ready to test their strength against the likes of Barcelona and holders Madrid, although he expects a difficult match at the San Paolo.
"I can see the progress the team has made," he said. "At the moment, we are doing very well against some good European teams. But the big tests are the big teams like Barca, Madrid, Juventus, Bayern [Munich] and Paris Saint-Germain.
"We are one of the top teams now but we have to prove it. I am very excited because we want to play Madrid and Barca to show where we are."
He added: "Playing in Napoli is horrible. It is so, so difficult for the opponent because the fans there are so good.
"The stadium is massive and the atmosphere is very intense. But I think we can play a good game like the one in Manchester.
"They came here and made it very difficult in the end, but I think we have a team that might be more dangerous away from home.
"When teams attack us, we can make the most of the space they leave at the back. With players of the speed of Raheem [Sterling], [Leroy] Sane and [Sergio] Aguero, we can attack the space."