The Dutchman is 7/4 favourite with Sky Bet to be the next Premier League manager to leave his post after the Cottagers' difficult start to the campaign took another bad turn on Tuesday evening.
After a comprehensive defeat to Southampton on Saturday, Fulham fell to an embarrassing Capital One Cup exit to second-tier Leicester at the King Power Stadium.
The bookies shortened odds on Jol leaving Craven Cottage immediately after the 4-3 defeat, although Press Association Sport understands he still appears to have the support of the Fulham hierarchy.
It is expected to be business as usual in the build-up to Saturday's clash with Manchester United, with the former Tottenham, Ajax and Hamburg manager set to face the media on Friday ahead of the match as planned.
Stopping the rot against the reigning champions on Saturday looks a tough ask for Fulham, who have lost all five matches against United since Jol arrived in June 2011.
To make matters worse, that match is followed by the unenviable task of a trip to Liverpool - a run of fixtures for which defeat to Sky Bet Championship side Leicester is hardly the ideal preparation.
Jol, though, remains resolute and insists he still has faith in his fringe players despite their latest defeat.
"We showed even with nine different players we were the better team in the second half and we should go to the next round but we didn't," he said.
"I trust them and I need to trust them and I want to trust them so that was not the problem because I really thought we had a good team out.
"I thought in midfield we had a couple of good players and I had a good bench - I thought Darren Bent could make a difference and Bryan Ruiz showed that he can make a difference so the scenario was okay.
"Giorgos (Karagounis) is a hero for me; he came in and worked his socks off and scored the third goal.
"Of course we've got other players who will come in again who were rested or injured. We had four or five who were injured and we couldn't play them so we had to change the team.
"A few boys showed they can play and they can play on Saturday I thought the spirit was good but we gave cheap goals away."
Leicester boss Nigel Pearson insists defeating top-flight opposition in the cup does not yet mean they have Premier League quality just yet.
The Foxes are promotion hopefuls again this year but their manager had some words of caution.
"This was a cup game," Pearson said. "I've played in many myself both as underdog and favourite and you will come unstuck in some and over-achieve in others.
"The league situation requires a level of consistency and a higher level of performance and ruthlessness that sometimes you can get away with if you play in the cup.
"We have had a stable squad of 18, 19, 20 for the last dozen or so games and it is always nice to start with the same XI.
"But if you do that you will have a number of players who don't have the pitch time they want or need and I don't expect to keep everyone happy but we have an ethic as a group in which they want to achieve.
"It is a bit different to what we've had in the past and I'm very happy with how we have progressed as a group.
"But I'm not a fool, there are areas we need to improve on and we don't keep enough clean sheets."