The Foxes have made an impressive start to life in the Championship after cantering to the League One title last year, sparking talk of back-to-back promotions.
And Gallagher, who moved to the Walkers Stadium from Blackburn in the summer, believes it can be done.
"We can achieve whatever we want," he told the Leicester Mercury.
"If you look around the squad there are decent players and, with the momentum of last season and the confidence, then we can achieve things.
"If you play with confidence then you can achieve whatever you want.
"With the momentum from last year, everyone is buzzing in the camp and we have had a great start to this season. I can't see why we won't be up there."