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.
"We will try to get one or two players in," Jol said of his January transfer plans.
"One example is right-back as Stephen Kelly, who went for a medical at Reading today. It is close to completion.
"I expect him to join Reading permanently."
Republic of Ireland international Kelly has been at Craven Cottage since 2009, making 71 appearances in all competitions.