Dalglish was a contender to replace Rafael Benitez at Anfield but has given his approval to the former Fulham manager, who took over at the Premier League club yesterday.
The Scot said in the Daily Mail: "I look very favourably on the appointment.
"I have known Roy a long time and have a great respect for him.
"We've not had detailed conversations yet but my interests are in Liverpool."
Hodgson is keen to retain the services of Dalglish - even though he was appointed to the top job the Scot was overlooked for.
Dalglish is currently involved in youth development at the academy and is an ambassador for the club.
"Kenny will play a very big part in bringing youth players through," said Hodgson.
"If he is going to take on the role of head of football development his role in making that bridge between Kirkby (where the academy is based) and Melwood (the first team training ground) is going to be a vital one.
"I think he has lots of other roles to play. With his position at the football club I compare him to Giacinto Facchetti at Inter or Bobby Charlton at Manchester United - they have such a role to play.
"When this club needs representing, especially on a foreign stage, who better to represent it than Kenny Dalglish?
"I am hoping that between those two roles, ambassador and head of youth development, and the advice and help he is going to give me in my job, we will get great currency out of Kenny if he wants to be part of that and I hope he does.
"I had a long conversation with Kenny before I got the job and we need to sit down together now to work out how it will work in practice.
"With goodwill on his side - and there is plenty of goodwill on my side - we should find a solution."
Chairman Martin Broughton was somewhat dismissive when asked about how Dalglish's expression of interest in the manager's job had been received by the board.
"Kenny put his name forward for wanting the job and we appreciated the fact he was keen to do it but for us he was never a candidate and I explained that to him," he said.
"We see Kenny as having an excellent long-term future at this club.
"He is happy in his current ambassadorial role but we would like to build on that role - although we haven't defined what that will be yet because it is for Roy and Kenny to work beyond that."
Hodgson said who the board chose or did not choose was out of his control but that in no way did he want to force Dalglish out of the club, quite the opposite in fact.
"Kenny Dalglish should be at Liverpool until he decides he no longer wants to be a part of football," added the former Fulham manager.
"I can't have any comment on the people who wanted to be candidates, it was up to the board to decide who they wanted and the chairman distinctly answered that question by saying they did not want Kenny to be a candidate for the job, but they do want him to be a part of the club today and in the future.
"They want him to use all of his skills to be part of the club long-haul to make sure we bring some players through."