The 25-year-old shotstopper was absent from Fulham's 4-0 Europa League qualifying victory over Crusaders as he concentrates on sorting out his future.
Fulham are keen to loan him out to a Championship club so they can include a recall clause in the deal.
"Yes, he is close [to a loan move] but of course there is a little issue with the recall," said Fulham manager Martin Jol.
"We can't recall him if he is playing in the Premier League. Maybe there is a bit of room for manoeuvre but I don't want to talk about it.
"[If we can't insert a release clause], then we have to put him in the Championship. But there is a possibility he could go to the Premier League."
Stockdale joined the Cottagers in 2008 from Darlington.