The Daily Mail report that the Cottagers remain hopeful of having a new manager in charge by the weekend with Eriksson's path to the Craven Cottage hot-seat clearing by the day.
With the claims of Switzerland and former Bayern Munich coach Ottmar Hitzfeld and current USA manager Bob Bradley falling away, Eriksson's status as the favourite to replace Roy Hodgson has been further enhanced.
Eriksson is understood to be the preferred choice of Alistair Macintosh, the Fulham chief executive, having worked with the Swede at Manchester City.