The 29-year-old was a key player for the Cottagers last season but has lost his starting berth to Sascha Riether this term. Kelly is set to leave the west Londoners in search of first-team football, with a permanent move to Reading close to completion.
Republic of Ireland international Kelly has been at Craven Cottage since 2009, making 71 appearances in all competitions.
Jol admits Fulham will have to be inventive, creative and lucky to get in players this month, with Tottenham's Tom Huddlestone and Dnipro midfielder Derek Boateng both on his radar. The Cottagers saw a number of key players leave in the summer and, after a bright start to the campaign, have dropped down the table.
"As a lot of other teams will tell you, we are very close [to bringing in players] but there are so many other teams involved," Jol said. "If you want a good player, other teams are there to try and jump on it so we have to be very inventive. We don't have a lot to spend, to be honest, so we have to be very creative."
Jol would not be drawn on links with Birmingham goalkeeper Jack Butland, but said there was no interest in Arsenal's Andrey Arshavin. The Dutchman was more forthcoming when it came to two midfielders at former club Tottenham, Jake Livermore and Huddlestone.
"Jake Livermore went to QPR, as you all well know, so he is off the list," Jol said. "Over the last six years I had an interest in Tom Huddlestone, but he was injured and then went to Stoke. I think he failed a medical there but I am not sure, so he went back to Spurs.
"If Tom is fit, he is always in the back of my mind but as I told you before, I won't speculate on names. I can't say Tom is not on my list because I like him. I always keep an eye on him, even when he is not coming here."
Jol has also been heavily linked with Ghana international Boateng, who currently plies his trade in Ukraine with Dnipro. "There is no movement there," Jol said. "I am not frustrated because of the reasons you think. Of course there are a lot of players that would probably make us stronger and we are not like Real Madrid, you know.
"We cannot offer £10million or £15million and get the players on the board. It is almost impossible so we have to not only be inventive, you need a bit of luck as well. That is probably the case now."