The 50-year-old has seen his side lose their last six consecutive Premier League games and is just 1/2 to be the first top-flight manager to leave
With two weeks until their next game, managers under pressure will be on high alert with regards to their futures.
Fulham's dismal start to the Premier League season continued as they lost 2-0 at Anfield in controversial fashion.
Aleksandar Mitrovic had a goal ruled offside and just 14 seconds later - with Alisson appearing to take the resulting free-kick while the ball was moving - Mohamed Salah opened the scoring for Liverpool.
The Cottagers were far from outclassed on Merseyside, but that was a sixth consecutive league defeat and the newly promoted club sit bottom of the table going into the international break.
Worryingly, Fulham have conceded 31 times in 12 games so far only one team - Barnsley (35) in 1997-98 - have ever leaked more at this stage of a Premier League campaign.
As a result, 888Sport make Slavisa Jokanovic 1/2 (1.50) favourite to be the first top-flight manager to leave this season.
There have been encouraging words from Fulham owner Shahid Khan in recent weeks and if the club decide to keep Jokanovic in place he could face a crucial showdown with Mark Hughes, who comes next in the market at 2/1 (3.0).
Southampton will feel aggrieved they didn't take three points from their clash with Watford having had a goal disallowed at 1-0 up and only taking a point from their meeting with the Hornets.
Saints sit 17th in the table and despite securing top-flight safety at St Mary's Stadium last term, the former Stoke boss will be expected to improve the clubs' fortunes sooner rather than later.
888Sport are finding it tough to split the sides ahead of their meeting at Craven Cottage which is their first game back following the international action concluding.
Fulham are 17/10 (2.70) to win the game with Southampton priced at 6/4 (2.50). The draw is available at 49/20 (3.45) with the same firm although that's unlikely to help either manager too much at this stage.
The sack race is seen as something of a two-horse race at this stage with Roy Hodgson, Jose Mourinho and Mauricio Pochettino all priced 14/1 (15.0).