Schwarzer, who almost left the Cottagers for Arsenal last summer, has again been in outstanding form for Mark Hughes's side this season to leave Stockdale without much first-team action.
Posting on social networking site Twitter, Stockdale recently said: "Hope I can challenge for No 1 spot next year. If not I will have to evaluate my future as MS (Schwarzer) is looking in good shape."
Following that statement, the former Darlington man insisted he will do all he can to force his way into the Fulham side but admitted, like any top footballer, he needs to play and may be forced to move elsewhere in order to get games.
"If people think I don't want to play for Fulham that's wrong! I WANT to play at Fulham for a long time! PLAY being the word," he added.
"It's not a threat not anything just my thoughts and I have two years on my contract."