Roberto Martinez's position at Goodison Park appears precarious following a season of underachievement, highlighted by supporter dissatisfaction in recent weeks.
Fans have held banners calling for the Spaniard to go and backed Leighton Baines after the left-back was forced to apologise for saying Everton lacked 'chemistry'. More protests are planned for Saturday's home game against Bournemouth.
Hughes, who had a brief spell as a player at Everton towards the end of his career, has been linked with succeeding Martinez but Stoke have indicated that they would not welcome an approach.
Hughes himself was unhappy at the way Manchester City sacked him in December 2009, approaching Roberto Mancini behind his back, and he said: "It's just speculation and I don't encourage that. Certainly not when someone is in the position.
"It's happened to me in the past when I've supposedly been under pressure at clubs and I heard other manager's names banded about and I didn't appreciate it then so I don't want to be part of that to be perfectly honest."
Asked if it was still flattering that his name was being linked with other jobs, Hughes joked: "On the back of three poor performances then it's positive speculation I suppose!"
Stoke have lost their last three matches and are without a win in the Barclays Premier League since March.