Crossley has been in fine form since moving to Hillsborough from Craven Cottage last month and Brian Laws has enquired about his availability should The Owls need it.
Currently, Crossley is only at S6 until the game with Hull City on New Year's Day but it is hoped that he can stay on, and even play a part against Manchester City in the FA Cup.
Laws said: "Things are looking very positive, but we are also keeping something else in mind for if Mark has to go back. We're letting things run for the next week or so. Fulham are quite happy so long as nothing drastic happens at their end."
Finnish star Antti Niemi is currently Fulham's first choice stopper with the Czech Jan Lastuvka waiting in the wings.