Fulham boss Martin Jol is keen to get the 25-year-old game time elsewhere rather being stuck warming the bench at Cottage Road.
Stockdale is behind Mark Schwarzer in the pecking order and the arrival of Hungarian keeper Csaba Somogyi has cleared him to move on.
Swansea have been linked with the Leeds-born shotstopper, but Jol refuses to loan him to another Premier League club as he cannot include a 24-hour recall clause in the deal.
The Cottagers goalkeeping coach Hans Segers revealed: "There is quite a few clubs interested and I can see something happening in the next few days. I'm waiting for confirmation from one of the clubs."