Hughes was sacked following Stoke's exit from the FA Cup to League Two side Coventry City on Saturday, and the club are ideally seeking an British manager to take over at the bet365 Stadium.
The Stoke Sentinel reports that former Birmingham City boss Rowett, 43, who has no Premier League experience, is being considered by Stoke owners Peter and John Coates.
Also on the shortlist is O'Neill, who has managed Leicester City, Aston Villa and Sunderland in the top flight and could combine the Stoke post with his Republic of Ireland job, should the Potters make a move for the 65-year-old.
The source also says, however, that Stoke are not expected to begin the search for a new boss until next week.
The club have a week to prepare for their fixture against Manchester United a week on Monday.