Derby County manager Gary Rowett and Republic of Ireland boss Martin O'Neill are the front-runners to take over at Stoke City, but foreign managers such as Ronald Koeman will also be considered, according to Sky Sports News.
The Potters acted to show Hughes the door on Saturday after Stoke suffered a humiliating FA Cup exit at the hands of League Two side Coventry City.
Stoke have now started the search for Hughes' successor as they bid to bring in a manager who can secure their status in the Premier League, and a British boss is favoured.
Derby manager Rowett is firmly on the club's radar, with the former Birmingham City boss having caught the eye with the work he has done at Pride Park with the Rams in the Championship.
Also a contender is Ireland boss O'Neill.
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The 65-year-old last managed in club football in 2013, when he was in charge of Sunderland.
But Koeman is also a possibility as Stoke refuse to rule out a non-British appointment despite their preference.
Manchester United legend Ryan Giggs also features prominently in the betting to take over at Stoke, along with former West Ham United manager Slaven Bilic.
