Rafael Benitez's eviction from the Anfield hotseat has created an attractive vacancy with the Merseyside giants that Hodgson has been tipped to fill.
"If the coach wants to be there he will be there," said Dempsey. "He has to do the best for him and his family."
The 63-year-old's star has risen dramatically over the last couple of years, first by keeping Fulham in the Premier League and then steering the Cottagers into Europe and, last term, into the Europa League final.
Little wonder Hodgson's name is near the top of Liverpool's hit-list, which could finally offer the former Switzerland coach a chance to make his mark with a big club in England.
Dempsey has starred in Fulham's attack and realises Hodgson would be a loss to the club, but the United States star has no intention of calling for his manager to stay.
He firmly believes if an offer comes, Hodgson should go with his heart.
Dempsey added: "It is not something I can worry about. I am with Fulham for three more years and I will do my best for them until something happens. If he wants to stay, let him stay. If he wants to go, let him go."