The midfielder has struggled for regular action this season, fueling talk of a move away, with the likes of West Ham and former club Fulham keen.
But lifelong Reds fam Elliott told the Liverpool Echo: "I hope that I can push on (next season). This is my team, I am committed to them and it's just a situation that is always going to have a lot of talk, I just need to think about what is best for my future, my career and as much as I want it to be here.
"You never know what is going to happen around the corner. If I had it my way, that would be here, I would play each and every game here and stay here for the rest of my career but it all depends on managers, the people above and as I said you don't know what could happen but as far as I am aware I am here, here to stay and this is the club I want to be at.
"Hopefully I am still here to be honest. It is the best place to be, the best club to be at and especially having the fans around us at the moment, I don't think there is a better place to be playing.
"Players go through ups and downs but at the end of the day you have to come out fighting and I think it is within myself to make it happen. So hopefully I can stay here for the rest of my career."