The Daily Express report that Butland, since joining the Potters, has only managed a handful of appearances due to the impressive form of Bosnian Begovic, leading to loan spells at Birmingham, Barnsley and Leeds.
Leeds United are currently in the market for a new shot-stopper, with Paddy Kenny the only senior 'keeper on their books, with Jamie Ashdown having been released.
Southend United goalkeeper David Bentley and Brazilian Heurelho Gomes have been linked to the Whites, although the latter has now joined fellow Championship side Watford.
The signing would also be a statement of intent for the club, especially if they could also hang onto key players, such as Sam Byram and Ross McCormack.
When asked about the possibility of another loan spell, he replied, “If Asmir stays and I’m not playing, a loan is massively important.”