Athole Still says the former England and Ivory Coast coach has "another offer on the table" but that "Fulham is an attractive club for anyone to go to."
Eriksson's short-term contract with Ivory Coast expired after the World Cup and Still said on Friday he would return to the Premier League.
Still added that Eriksson was still unhappy at being fired by Manchester City two years ago after one season.
Fulham is still looking for a successor to Roy Hodgson after Ajax refused to release Martin Jol from his contract on Thursday.
Cardiff's David Jones has also been linked with the position but the English second-tier side has received no approach.
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