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.