The two sides meet at Loftus Road on Saturday, with the Cottagers fresh from an overdue win over Newcastle United, and the boss hopes to extend the Rs winless streak
The two former Tottenham managers face each other this weekend and Jol highlighted the Rs unbeaten start to life under Redknapp as cause for concern ahead of the clash at Loftus Road.
Jol told reporters: "I can remember from even before Harry was there when they were quite close to winning.
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"Harry has been there a couple of weeks now, and they are looking for a response all the time and need a response now. We are aware of that. I think they have got the quality and, of course, Harry is capable of coming up with a few very good results."
Jol has experience of taking over a struggling side with RKC Waalwijk – his employment before moving to Tottenham in 2004 – and managed to avoid relegation despite a poor start to the season.
The Dutchman sympathises with Redknapp, but hailed his "fantastic" abilities.
He added: "I think [taking over at a struggling team] is always a tough job.
"At my second club, they had three points at the end of November and that was the first time in history that a club had that amount of points and still managed to stay in the league.
"The year after, we were fourth with two other clubs, so I think Harry can do a similar job. He's proved in the past that he's a very good manager, a fantastic manager, but it's a big challenge."