The 19-year-old made his England debut against Italy earlier this month and has long been linked with a move away from the Blues.
Butland, quoted in The Sun, said: "There is nothing more important for me at the moment than staying put and playing games.
"I'm still only 19 and there is no rush. I don't know how many 19-year-olds are playing in the Championship - there's certainly not many in the Premier League.
"I know I have the chance to play games here and that's important. Hopefully it will keep me in the England set-up.
"If I was to move and I wasn't getting games, it would hit my chances with the international side."