The 20-year-old signed for the Potters in January and subsequently spent the remainder of the season on loan at Birmingham City, the club from whom he joined.
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"That's the aim [to be No.1]," he told the club's official website.
"I know that won't be easy because Asmir is a top, top goalkeeper and has done really well for Stoke City in the past but I'm excited about the challenge.
"I'm settling in very well. I came in a few times in the second half of the season, which helped me get to know the lads and made it a bit easier when we reported back.
"I'm getting on with the lads and enjoying the training."
Butland played every minute of Birmingham's Championship campaign last term and made his senior international debut for England in a friendly against Italy in August 2012.