It is understood that the terms on offer include a fee of just under £4million and the option for players to join the Blues on loan - with Ryan Shotton among those Stoke would be prepared to part with.
The Birmingham No.1 turned down a move to European champions Chelsea earlier in the week over fears he will not play regular first-team football at Stamford Bridge.
And despite reported interest from Fulham, Tony Pulis seems determined to bring the 19-year-old, who made his international debut in England's 2-1 win over Italy in August, to the club.
The Potters boss currently has Asmir Begovic and Thomas Sorensen at his disposal already and if Butland does make the move to Stoke, the club could loan him back to Birmingham for the rest of the season.
The shot-stopper has also been linked with Liverpool, Newcastle and Manchester City, while Southampton and Everton attempted to sign him last summer.
Sky Bet initially installed the Reds as the favourites to sign Butland but Stoke have since been backed into odds-on to secure his services in their Transfer Specials.