Rafael Benitez left Liverpool on Thursday by mutual consent and will be unveiled as Inter manager in the coming days.
The bookmakers have made Roy Hodgson their favourite to take over at Anfield, while Martin O'Neill has also been touted as a possible replacement.
Liverpool ambassador Kenny Dalglish has been put in charge of finding Benitez’s successor and it is believed that his friendship with Hodgson could prove pivotal to the Fulham boss being approached by the club.
Dempsey, who has thrived at Fulham under Hodgson, believes Hodgson should be allowed to succeed the Spaniard if an offer is tabled.
"Hodgson must be given the chance to succeed Benitez if an offer comes in," Dempsey said, according to Sky Sports News.
Dempsey is likely to start for America in their opening World Cup 2010 fixture against England on Saturday.
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