Hughes is just over halfway through the three-year deal he signed on replacing Tony Pulis in the summer of 2013.
And a source at Stoke confirmed the club’s board is keen to extend his deal in the medium-term – probably by a further two years.
Hughes oversaw a ninth-placed finish in last year’s Premier League, and wins against Manchester City and Arsenal this season have helped City to 10th after 22 games.
The source said: “We’re really pleased with job Mark Hughes is doing. It’s a good fit, and we hope he stays with us for many years to come.”