Jol is likely to include his most recent signings, Darren Bent and Scott Parker, in his side against Arsenal, when the Cottagers look to add to their opening day victory over Sunderland.
"You don't know what will happen because we have still got 10 days to go, and maybe we are one or two players short," Jol said.
"But if it stays like it is now I think we can be quite happy because if you would have told me three or four weeks ago that Darren Bent would be on board, as well as Scott Parker and also Adel Taarabt, who played for me at Spurs and was a £15m player (at QPR) probably 18 months ago, I wouldn't believe you, so I am a happy man."
Jol thinks Parker will turn out to be an excellent signing for the club, who he chose ahead of a drop down to the Championship with QPR.
"Scott is the perfect player for most of the managers in the Premier League," Jol added. "He is English, is a leader, can play on the ball, can play off the ball, and he makes interceptions, so I think it is fantastic to have him on board."
But he knows Arsenal will provide Fulham with a very tough test, after they put aside all talk of panic in the ranks over their lack of summer signings by thrashing Fenerbahce in the Champions League on Wednesday.
He concluded: "I played in Turkey a couple of times and it is almost impossible to have a win over there and they did, quite convincingly.
"They played with confidence, they were very sound at the back, in midfield they were very creative, they had pace up front and with their chances they could have scored more goals, so I am not sure if they have got a problem.
"There is not a fear factor in our team about Arsenal, but of course you know their qualities and you have to respect their qualities and try to play your own style."