The 33-year-old former Manchester United striker is available for a move having failed to make an impact at St Andrews.
But Yorke is currently in his native Trinidad considering a transfer to Australia, and looks unlikely to move to west London.
Meanwhile, West Brom midfielder James O'Connor has been identified as a possible alternative to Bristol City's Tom Doherty, who Rangers have tried in vain to sign.
But again a deal before today's 5pm deadline looks unlikely, and Rangers' only expected signing is that of teenage defender Dominic Shimmin from Arsenal.
Tony Thorpe has completed his loan move to Rotherham.