The Potters reportedly see the former QPR boss as a good fit at the Britannia Stadium, where the resignation of Tony Pulis by mutual consent has attracted a number of applicants
The Potters' hierarchy apparently see Hughes as a good fit for the club, and have made their interest known to the Welshman, though they have not ruled out other candidates, with Wigan boss Roberto Martinez also believed to be under consideration.
However, the 49-year-old former Manchester United and Chelsea forward, who was sacked by QPR in November, appears to be in pole position to fill the vacancy at the Britannia Stadium created when Pulis resigned on Tuesday after seven years at the club.
The striker who also enjoyed spells at Barcelona, Bayern Munich, Southampton, Everton and Blackburn has enjoyed a somewhat mixed career in management so far, having begun it unusually in 1999 by taking charge of the Wales national team before gaining experience at club level.
His creditable performance managing his country earned him the Blackburn job in 2004, and four years later he moved to Manchester City, but was dismissed after 18 months and replaced by Roberto Mancini.
Hughes then spent one season as manager of Fulham before resigning, saying: "As a young, ambitious manager I wish to move on to further my experiences".
He was appointed as QPR manager in January 2012 and helped them avoid relegation last season, but was sacked three months into the 2012-13 season after 12 games without a win - the club's worst start to a Premier League campaign.
Stoke are expected to begin formal talks with several managerial candidates within the next few days.