Following a ninth-place finish in the Premier League last time out, manager Brendan Rodgers has spoken publicly about his desire to break into the top-flight's upper reaches.
With City enjoying victories over Manchester City, Chelsea and Arsenal last term, Walsh says Rodgers' men can now approach the new season with excitement.
"I believe now that the Club has a manager who is young and ambitious and a man who can bring the right kind of energy which Leicester needs," the two-time League Cup winner said.
"Last season was one in which some of the supporters would obviously have liked for us to be a little bit higher in the league, but progress was made on the football pitch.
"We beat some of the top teams. Admittedly we also slipped up against some of the others, but we’ve built a really talented squad who can push on now.
"They can beat anyone on their day, there’s no doubt about that, and I like the style of football which Brendan is trying to bring to the Club."
Leicester are in possession of one of the most talented and youthful squads in the Premier League, a crop full of exciting prospects for the future.
Walsh says those youngsters are now ready to propel City to the 'next level' and mount a serious challenge to secure qualification into a European competition next season.
"The players who the Club already have and the ones who they will try to sign in the summer could really take the Club to the next level," he continued.
"There’s a lot of mileage in the youth policy at Leicester City at the moment and it’s great for the future so the Club is in a very, very good place.
"I’m really upbeat about the new season. I’m looking forward to the new fixtures coming out, the new kits are already here, and there’s a lot of optimism for the new season.
"It’s going to be an exciting season for Leicester City. We’re trying to get to the next level and everything about the Club is going in the right direction, including the football side of things."
Walsh, who spent 14 years at the Club and continues to support Leicester, also reserved praise for Rodgers' impact at the Football Club since his appointment in February.
The 54-year-old says the former Liverpool and Celtic manager has implemented a vision for the Club which all supporters can back wholeheartedly during the upcoming campaign.
"Brendan’s philosophy and the style of play he wants to see is positive, the attacking style of football, and he simply wants to play football in a manner of pressing and going forward," he added.
"That’s why I’m so excited about next season. Obviously everyone is aiming for top six but I think they can push for even higher.
"There’s a few clubs in the top places who could be exposed a little bit next season and I see no reason why Leicester City can’t be the team to leapfrog them in the table."