BBC Sport reports.
The Championship side are keen to sell the 19-year-old in January because of their financial problems. Butland is likely to be loaned back to Birmingham for the remainder of the season if the deal does go ahead.
Birmingham also hope to sign a couple of Stoke City players on loan until the end of the season as part of the Butland transfer.
Butland has already rejected talks with Chelsea over a £3.5m move because he wants regular first-team football. He has also been linked with a move to Liverpool, Fulham, Newcastle and Manchester City, while Southampton and Everton tried to sign him last summer.
The keeper played for Great Britain at the Olympics and made his England debut in the 2-1 win over Italy in August. Butland was also called up to the England squad for Euro 2012, after third-choice goalkeeper John Ruddy broke a finger, even though he had spent the season on loan at League Two side Cheltenham.