According to the Sun, the 59-year-old is keen to return to the top-flight after being sacked by West Bromwich Albion last month and could return to the bet365 Stadium for a third spell, should Stoke chairman Peter Coates opt to relieve Hughes of his duties.
A dismal run of results has seen the Potters plunge to 17th in the table, just one point above the relegation zone, after losing five of their last six Premier League games and Hughes' future is now in severe doubt.
The Welshman's style of football has been subject of intense criticism from the fans, who made their feelings known as Stoke slumped to a 3-0 defeat on home turf against West Ham United on Saturday (16 December).
Pulis' second spell in the Potteries ended in May 2013, when he left the club by mutual consent after seven years. Under his stewardship, Stoke reached the Premier League for the first time in their history after finishing runners-up in the Championship in the 2007-08 season.
The report adds the relationship between the former West Brom manager and Coates has remained friendly even after the former's departure but while Pulis is understood to be open to the idea of returning to Stoke, he has made clear he wants to spend Christmas at home with his family.
With Pulis at the helm Stoke never looked in any danger of being relegated but they also never finished above 11th, while Hughes guided them to three consecutive ninth place finishes in his four seasons at the club since he replaced his countryman.
However, the latter now appears to be on borrowed time and could be sacked if Stoke fail to beat West Brom at home this weekend. The clash with the Baggies, who are currently second from bottom and without a win since the second weekend of the season, comes before potentially very difficult trips to Huddersfield Town and Chelsea before the end of the year.
Despite the lack of results, Stoke captain Ryan Shawcross insisted the players were still firmly behind Hughes.
"That's the game we're in and the manager knows it," the 30-year-old was quoted as saying by Sky Sports. "He knows we need results. If we stick together as we have done over the years then it helps a lot.
"We know he's a quality manager, we believe in him. Unfortunately we are going through a bad period at the moment but, as we've shown over the five years he's been here, I think he's been one of the most successful managers we've ever had as a club."