Gascoigne was caught on camera impersonating a flute player as he warmed up during the second half at the Old Firm game on New Years Day.
Farry is threatening to discipline Rangers and the England midfielder unless the Scottish champions take appropriate action. He also suggests the club should make the punishment public.
"Gascoigne's action was unprofessional and inflammatory," Farry said. "Having been down this road before I wonder to what extent the association's signals to club and player have been heeded. If necessary then I am in no doubt that the association will bring this message home graphically."
Michael O'Neill is ready to make his debut for Aberdeen at Ibrox today after the Northern Ireland midfielder came through a reserve match on Wednesday unscathed.
O'Neill joined the Dons on a three-month loan deal from Coventry last week but was unable to play because his clearance had not been received in time.
Dunfermline face bottom club Hibernian at Easter Road without a win since the middle of November but their assistant manager, Dick Campbell, remains optimistic. "We know that a couple of wins will send us back up the table and that is what we are striving for," he said.Reuse content