The Cottagers travel a couple of miles up the road on Saturday afternoon for a west London derby with more riding on it than most.
QPR have yet to secure a Barclays Premier League victory this season, with their 16-match winless streak an all-time Premier League record.
That abysmal start leaves QPR bottom of the table but Jol believes anything is possible with Redknapp at the helm, highlighting an unlikely turnaround he oversaw when at the helm of RKC Waalwijk.
"At my second club they had three points at the end of November," the Dutchman said.
"It was the first time in history that a club had that amount of points and we still managed to stay in the league so that was good.
"The year after we were fourth with two other clubs so I think Harry can do a similar job.
"Harry has proved in the past that he is a very good manager, a fantastic manager, but it is a big challenge.
"I had the same in Holland so you can never write clubs off. I think they have got the quality.
"Do they have the mentality? I think it is something which is written in the stars but I think Harry is capable of coming up with a few very good results and then for them hopefully keep them up."
There was much expectation around Loftus Road this summer, with the club bringing in a host of big names to avoid a similar relegation scrap to the one they endured last season.
Asked if he had been surprised the failure so far at QPR, Jol said: "Yeah, I really thought with the players they got in, with the money they spent (they would kick on).
"Of course we were involved as well. Our players (Bobby Zamora and Andrew Johnson) went over there and I think they did a lot to get these players. It wasn't just seven or eight it was at least 12, 13 or 14 players.
"If you change your whole squad around you feel you are improving all the time and they still probably got less points than they had last year so of course I am surprised."
While it might be all the doom and gloom at their west London rivals, Jol will not be taking them for granted.
The Fulham boss was quick to highlight the fine line between success and failure in the Premier League epitomised by QPR's seven draws to date.
"Harry has been there for a couple of weeks now and they felt they need a response all the time," Jol said.
"They need a response now, we are aware of that. But they were quite close all the time even before Harry was there.
"They have seven draws so they could have had wins because I saw a couple of games where they were very unlucky with red cards.
"Not only once but twice or three times so they are in a difficult situation, but I feel there is a lot of games to go.
"You can get a lot of points on the board so you can never write them off."