A formal address to Parliament is associated with this type of visit, but there had been reservations from some about the US President being able to do so on his visit.
Mr Hunt has, however, backed calls for Mr Trump to be given the opportunity, claiming the most appropriate thing to do would be to give Mr Trump “the best possible welcome”.
The announcement of Mr Trump's trip has sparked a row between Commons Speaker John Bercow and his House of Lords counterpart Lord Fowler.
Mr Bercow said in 2017 he was "strongly opposed" to granting the President the honour of a speech to MPs and peers in the historic Westminster Hall because of his controversial ban on migrants from certain Muslim countries.
But Lord Fowler said he would have to discuss any request to speak with Mr Bercow, adding that there was "a strong case" for a speech by the President, particularly as his visit coincides with the 70th anniversary of D-Day.
Asked at a Westminster lunch whether he would support an address to Parliament, Mr Hunt said: "Yes I would.
"I think it is very important when you have a state visit by our closest and most important ally that we think about the office as much as the person.
"I hope we make the best possible welcome for President Trump. He is a controversial politician, but in the end his visit is about more than Trump's policies, it is about the alliance between the United States and United Kingdom that goes back many, many years.
"The appropriate thing to do is to show him the best possible welcome."
The speakers of both Houses of Parliament have said that no request has yet been received for Mr Trump to speak in Westminster Hall. Downing Street says it has no control over the decision, which is a matter for Parliament.
Mr Hunt's comments came as Liberal Democrat leader Sir Vince Cable revealed he has turned down an invitation to a state banquet with Mr Trump at Buckingham Palace.
In a letter to Palace staff, Sir Vince said, "I have taken the view that as a party leader I should not support state visits where the government of the day has issued invitations inappropriately.
"I did not accept an invitation to attend a state banquet with the King of Saudi Arabia for that reason. I hope and trust Her Majesty The Queen will understand that I decline this invitation out of no disrespect to her. I am of course hugely honoured to have been invited."
The Lib Dem leader later said the UK should not be "rolling out the red carpet" for "a man who is on record as a misogynist and a racist".
"The fact this state visit is occurring at all is a shameful stain on the Government, who doubtless see it as a distraction from the mess they are making of running the country," said Sir Vince