The 27-year-old, who joined the Magpies in 2011, got his chance to impress at the end of last season following an injury to Krul.
However, Elliot is now keen to cement his place between the sticks at St James' Park after falling back down the pecking order.
"Tim is a top keeper and he is the number one, but I am not here just to sit on the bench," he is quoted as saying by Sky Sports News. "I am here to push him.
"That's what I did all pre-season and I was disappointed, to be honest with you, not to start the season.
"Obviously, Tim has been fantastic, as he usually is. All I can do is back it up when I get a chance to play and keep doing well in training."
Newcastle return to Premier League action on Saturday when they travel to Aston Villa.