The Cottagers manager believes their west London rivals have every chance of surviving in the Premier League and will not underestimate the threat they pose in Monday's fixture
Jol has been impressed by the relegation strugglers' recent results and will not underestimate Harry Redknapp's team when they visit Craven Cottage on Monday evening.
"QPR played against Sunderland and they won," he told Fulham's official website. “Southampton away from home - it was not easy, but they beat them.
"Chelsea, although it's a bit longer ago, they beat them away from home. The only thing was [the loss against] Aston Villa in their last match.
"Before that they had draws against Norwich and Spurs, so they've had good results. If QPR manage to win four or five games then they've still got a good chance of staying up."
The Cottagers could put a dent in their rivals' survival hopes but Jol would not be drawn into predicting which club would face the drop come May and was keen to see his own side ensure their top-flight safety.
"I don't want to talk about that because we need a couple of wins," he continued. "I've got no preference who stays up.
"If I say I hope QPR stay up then that probably won't do Norwich City a favour, or Stoke City who are still in that mix, or my friend from Wigan Athletic [Roberto Martinez] who is an unbelievably good guy.
"So I won't say that I would like QPR to go down because I like Harry Redknapp - he's a fantastic man and a good manager. At the end, the league won't lie, the rankings won't lie.
"That will be the thing. QPR will fight until the end because there are 24 points still to play for, and that is a lot."