The 28-year-old has been allowed to leave Craven Cottage on a regular basis in the past - taking in spells at five different clubs in the last five years.
Stockdale has had to go in search of regular football elsewhere after seeing his route to the Fulham first team blocked by Mark Schwarzer.
The experienced Australian moved on over the summer, but Maarten Stekelenburg has been drafted in as his successor.
An injury to the Dutch shot-stopper at the start of the season offered Stockdale a rare nine-game run in the side, but he has since been dropped back to the bench.
Another loan switch has been mooted, but Jol will only sanction an exit if he can bring in cover when the transfer window re-opens.
He said in the Fulham Chronicle: "Stockdale has played a lot of games in the Premier League and was fine at the start of the season.
"Last time (when he was dropped) he was probably not as happy as I hoped he would be but, on the other hand, he's ambitious because he wants to be in goal.
"If I had another very good goalkeeper I would probably send him on loan."