Reds co-owners George Gillett and Tom Hicks appointed Barclays Capital in May to sell their control and British Airways chairman Martin Broughton was appointed to oversee the process.
Broughton confessed on Thursday at a press conference to unveil Hodgson as Rafa Benitez's successor that he had yet to receive an official offer for Liverpool, but he insists that there are interested parties.
With Liverpool struggling under reported debts of £350million, Hodgson wants to see the arrival of replacements for Gillett and Hicks, and to get his hands on the expected transfer funds that would be made available after a takeover.
He said: "The sooner that happens the better. That is what the fans want. They want new ownership, maybe in the way Manchester City found new ownership!
"I can understand fans wanting that because they want the best for the club.
"They know the only way to get that is to have quality players on the pitch and they cost money."
Former Fulham boss Hodgson was made aware of the structure and status of Liverpool's hierarchy before he arrived.
He added: "It was made clear to me how the board was set up and that the owners are quite prepared to sell the club.
"I was told I would have to accept that somewhere during my tenure the club might be sold and I fully understand the position.
"There's always going to be people who want to own Liverpool. It's just a question of when it can be sold and whether the new owners are prepared to back the club as we all think it should be backed."