Fulham can sign Sami Hyypia - once Liverpool find a replacement for the veteran Finn.
The Sun says Fulham chief Lawrie Sanchez has already had one bid knocked back.
But Benitez knows the big Finn is keen for a move to Fulham.
It would guarantee him regular first-team football and see him link up with his friend, Antti Niemi - who will be fit in a week after scans revealed he has not broken his wrist.