Stockdale joined Hull last month on a deal until 2nd January, but Steve Bruce is keen to keep the goalkeeper at the KC Stadium for longer.
Jol is willing to let the 27-year-old stay with the Tigers as it would benefit him to play regularly in the Championship.
However, Jol has no intention of leaving himself short of options and has made it clear that Stockdale would be recalled if anything happened to Schwarzer.
"As long as Mark is fit he will stay there," Jol said in the Fulham Chronicle.
"We have a recall clause and if necessary we will get him back. If not, then he will stay there."
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