Due to Birmingham’s current financial situation, the 19-year-old is believed to be available for as little as £3m.
This has alerted Potters boss Tony Pulis, who is thought to be searching for a replacement for the much sought after Asmir Begovic.
Both Manchester United and Manchester City want the Bosnian international and are believed to preparing summer bids.
Butland could be an ideal long-term successor, so Pulis is tempted to strike whilst his value is low.
It is unclear as to whether he would be willing to wait until next season to be first choice, but regular game time would be far from guaranteed at Liverpool or Fulham.
The teenage stopper was a part of England’s EURO 2012 squad, following a successful season in the Championship last term.
He did not feature at the tournament, but was a key player during Team GB’s Olympic campaign, for which he was also chosen.
Southampton made an official bid for Butland over the summer, but Birmingham rejected their £6m offer.