The People says Liverpool managing director Christian Purslow has received a glowing recommendation about Hodgson from former Anfield boss Gerard Houllier.
And Fulham have now put transfer and contract talks on hold until his future is sorted, as they believe their hugely successful boss is on his way to Merseyside.
Kop legend Kenny Dalglish has now withdrawn his interest in taking over as manager. And Liverpool are poised to make an official approach, opening the door for talks to start in the next few days.
Agents working on deals to bring players to Fulham, and those hoping to renegotiate existing contracts, have been told they must wait until Hodgson has spoken to Liverpool.