City made it to the semi-finals of the competition last season under Manuel Pellegrini - the most advanced stage they have ever reached - but lost 1-0 over to legs to Real Madrid, who went on to lift the crown.
They already have a foot in the quarter-finals this season as they hold a 5-3 lead heading into the second-leg of their second round tie against Monaco.
Guardiola has set all types of records throughout his career, winning 14 trophies at Barcelona - including two Champions League titles - and seven at Bayern Munich, but leading City to the top of the European summit would top the lot, according to veteran midfielder Toure.
"I think this could be Pep's biggest achievement," said Toure. "It is his biggest test. But this guy likes challenges – and so do the players. So it is good.
"This team is so young. We already had good players, but now Pep brings in young players and that is so demanding for him.
"But it is starting to feel like something big is happening at City. The fans feel it, everyone feels it.
"We are getting a winning mentality in Europe and playing very well. When we play like we did against Monaco, we come close to the great teams like Real Madrid, Barcelona and Bayern. We cannot dream about anything yet because we still have a second leg to play," Toure added.
"But if you ask the fans, they believe it. You saw their reaction against Monaco."