The 20-year-old joined Stoke from Birmingham City last January, but was immediately loaned back to the St Andrew's club for the remainder of the season.
With Bosnia-Herzegovina international Asmir Begovic firmly established as Stoke's number one, Butland has had to be patient when it comes to first-team opportunities in the Premier League.
After a loan spell at Barnsley earlier in the current campaign, Butland was given a chance by Stoke boss Hughes in January after both Begovic and Thomas Sorensen picked up injuries, and the youngster impressed in four appearances.
However, now that Begovic and Sorensen are fit again, Stoke appear happy to let Butland gain first-team experience elsewhere as he seeks to keep alive his hopes of being selected in England's FIFA World Cup squad.
Speaking at a press conference on Thursday, Hughes confirmed Leeds were close to securing Butland's services.
"I think there has been contact with Leeds regarding Jack Butland, and we are hopeful of a loan deal being concluded," said the Welshman.
A regular member of England's Under-21 side, Butland has one senior cap - gained in a friendly against Italy 18 months ago - and also played for Great Britain in the 2012 Olympic Games.
