The 20-year-old has been amid reports that the Potters are willing to send him out on loan following his move to the club from Birmingham City last season.
"I know that [challenging Begovic] 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," Butland told the club's official website.
"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 signed for the Potters in January, but spent the remainder of the season on loan to the Blues.