Hughes' final game in charge of Saints was a 2-2 draw against Manchester United – meaning the Red Devils have failed to win in their last three league games.
Mourinho is now just 5/4 to be the next Prem manager to leave his club with 888 Sport.
The Special One has seen his side struggle in the English top flight after losing to Man City 3-1 before drawing to both Crystal Palace and Southampton as they trail fourth-placed Arsenal by eight points.
An 888sport spokesman said: “Hughes and JoseMourinho were in opposite dugouts on Saturday, but after the Welshman was fired this morning, the same fate may soon fall on Mourinho.
“We now make Mourinho the new favourite to be the next manager to lose his job – and with a tricky match against Arsenal on Wednesday, it could be days rather than weeks until that happens.”
888 Sport: Premier League sack race
Jose Mourinho 5/4
Nuno Espirito Santo 4/1
Rafa Benitez 6/1
Sean Duche 9/1
David Wagner 11/1
Neil Warnock 14/1
Mourinho has publicly had feuds with a number of key players this term, after calling out the likes of Paul Pogba and Anthony Martial.
Following United's draw with Saints, the 55-year-old reportedly called Pogba "virus" in front of all of the players.
This comes after Mourinho also said the World Cup winner was no longer fit to skipper United.
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