The Cottagers manager is the No1 target for Liverpool to succeed former manager Rafa Benitez.
But the Fulham & Hammersmith Chronicle says a rock-solid source close to the 62-year-old dismissed speculation linking him to the post as successor to Benitez - ousted from Anfield last Friday.
The source said: "No one from Liverpool, or connected with them has spoken to Roy - and he is mystified by all the conjecture over the last few days."
Hodgson has hinted he would be in west London for campaign number three after welcoming his first signing of the summer on Tuesday when Philippe Senderos arrived from Arsenal.