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."