The 49-year-old headed into the weekend as the 6/4 joint favourite to be the first Premier League manager to go along with Saints boss Nigel Adkins, who has been pushed out to 12/1 following a first away league win this season.
A 12-match winless run has seen the Hoops cut from their pre-season price of 4/1 to 8/11 for relegation, while Harry Redknapp is rated as Hughes' most likely successor with QPR the1/4 favourites to be his next club.