The Cottagers still haven't given up hope of keeping Hodgson away from Anfield with so much uncertainty over the future ownership of the club and limited transfer funds available.
But Fulham are making contingency plans should Hodgson depart and Eriksson has emerged as a strong contender.
Chief executive Alistair Macintosh worked with the former England boss for a season at Manchester City before both men lost their jobs in the summer of 2008.
He is a big admirer of a manager who won championships with Gothenburg, Benfica and Lazio and who took England to successive World Cups.