Cahill visited the Holy Family Primary school in Halewood last week.
He was there as part of a Barclays Premier League initiative to promote community sports projects.
"The feeling is really positive around the club at the moment, even if the results haven't quite shown it," Cahill said. "Lots of people are suggesting we now have a stronger squad than Liverpool, and you know what, it could well be true.
"We have such a belief in ourselves right now, we don't have to go through that thing of comparing ourselves to our neighbours.
"That isn't the limit of our ambition because we've got such a great squad. I believe we have got a massive chance to do something really big this year, and that is our focus.
"Maybe it would be foolish to aim for a top four finish, but it's realistic to aim for the top six and then beyond that."