The former England and Manchester City boss is Fulham's first-choice option after the expiry of a break clause in Jol's contract brought an abrupt end to their interest in the Ajax chief.
Fulham's hierarchy were forced to admit defeat in their pursuit of Jol after the Amsterdam club stood firm in their refusal to allow the former Spurs boss to quit.
With the start of the Barclays Premier League season just three weeks away, Fulham have wasted little time moving on and the Swede will now be approached to replace Roy Hodgson.
Eriksson does have significant support at the club and it is understood owner Mohamed Al Fayed and chief executive Alistair Mackintosh were originally split on who should take over.