The Potters sit ninth in the Premier League, trailing fifth-place Manchester United by just four points, and reached the League Cup semi-finals, suffering elimination on penalties at the hands of Liverpool on Tuesday night.
Reports have claimed Hughes features on a list of domestic targets that also includes Claudio Ranieri and Eddie Howe should Chelsea miss out on leading candidates Massimiliano Allegri, Pep Guardiola and Diego Simeone.
"There is always speculation like that," Hughes said ahead of his side's FA Cup fourth-round tie at Crystal Palace.
"When you have a decent spell your name gets mentioned and this week it is me, but it is what it is. There is so much speculation going around and people being linked with different jobs in the country."
Hughes says Stoke are keen to add to their squad before the close of the January transfer window but will not be rushed into panic buys if they miss out on their preferred targets.
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"We would like to add if the right person is available and we can bring him to the club," he added. "There is a danger sometimes that you start scrambling around trying to do business if your 'A' targets fall by the wayside.
"There will be no hurried decisions and no last-minute deals which we have not done work on before and considered."
Hughes continued: "I thought we did really well [against Liverpool] and obviously everyone is disappointed not to go through.
"Tactically our work was spot on, we played better football and created better chances. Unfortunately we lost the first tie, won the second tie but lost on penalties.
"It was the first time we have won at Anfield in 50-odd years so that is something to take from the game."