Scharner's agent Valentin Hobel said: "Aston Villa wanted him as a defender and that is why they are no longer an option.
"Fulham are strong at the moment. However, there is still the possibility he could go to Germany with Hamburg.
"He will look at his options very carefully.
"If they can offer concrete figures and everything else all fits into place, then it could happen quickly and all be concluded within a week."