Hughes, the former Wales, Blackburn, Manchester City, Fulham and QPR boss, is the favourite for the post vacated by Tony Pulis last week.
Stoke have also been linked with Roberto Martinez, who is to leave Wigan and has been given permission to speak to Everton, but discussions with 49-year-old Hughes are believed to have taken place.
Hughes has been out of work since he was sacked by QPR last November.
The Potters parted company with Hughes' fellow Welshman Pulis by mutual consent after seven years together last Tuesday.
Chairman Peter Coates said the club were intending to move in a different direction.
Pulis guided the club into the Premier League in 2008 and they have stayed there since, also reaching the FA Cup final in 2011 and subsequently playing in the Europa League.
For Hughes, Stoke may present a challenge similar to that he took on at Blackburn, whom he led to three successive top-10 Premier League finishes and two FA Cup semi-finals before leaving in 2008.
He may also welcome the stability that life at the Britannia Stadium would seem to offer after the uncertainties of Loftus Road. Hughes might also be able to work better with the Potters' current squad of players than Martinez, although the suggestion is the club want to tone down the robust style of old.
Pulis certainly started to come under fire from fans in the latter months of his reign over a perceived lack of development.