The Daily Star report that the Swede remains Fulham's No 1 choice but fears his reputation will ruin his chances of succeeding Roy Hodgson as Craven Cottage boss.
Eriksson is prepared to take a drop from the £3m a year he received at his only previous Premier League job at Manchester City.
Eriksson has been incensed by reports that his wage demands are threatening to scupper a move to west London.
The club have made initial contact with Eriksson's agent Athole Still and the 62-year-old does want the role.