Stockdale has been linked with a move to the Liberty Stadium, but the Cottagers have ruled out allowing him to join a Premier League club as they cannot insert a 24-hour recall clause in the deal.
That means the 25-year-old will have to drop down a level if he wants to secure regular first-team football.
Fulham goalkeeping coach Hans Segers told the Fulham and Hammersmith Chronicle: "There are 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."
Stockdale will be allowed to depart on loan as Martin Jol has already recruited a back-up shot-stopper in the shape of Hungarian keeper Csaba Somogyi. The 26-year-old's move on a free transfer from Budapest outfit Rakospalotai EAC was confirmed by Segers after Saturday's friendly against AFC Wimbledon.
Segers said: "Somogyi's signed for us now. I had him on a five-day trial and he made a very good impression. That means we can lend David Stockdale out because he needs to be playing every week.
"It's a big step up for Somogyi because he was playing in the Hungarian second division but he's a very good goalkeeper."
Meanwhile, Jol should tie up the transfer of former Liverpool left-back John Arne Riise after the Roma man undergoes a medical on Monday.
Jol told the Chronicle: "He had a very good season and I'm very pleased a player like him has joined us."