Mr Albanese described the private audience he had with the King at Buckingham Palace, on Tuesday, as "very warm".
"I appreciated the discussion that we had and that King Charles has a great love for and affection for Australia," Mr Albanese told reporters while visiting Barrow-in-Furness in northern England on Wednesday.
"It comes from his time as a student there but also his many visits to Australia."
Mr Albanese, a republican, said he was looking forward to being at the monarch's coronation ceremony on Saturday and that the King was "very familiar with the range of issues that Australia is facing".
The prime minister said he had extended an invitation to visit Australia during the meeting.
"I can confirm that I once again reiterated that King Charles and Queen Camilla would be very welcome visitors to Australia as would any other member of the royal family."
Mr Albanese is among a contingent of Australians invited to the coronation along with Governor-General David Hurley and state governors.
The Australian delegation includes Matildas captain and football star Sam Kerr, singer Nick Cave, Aboriginal artist Jasmine Coe, comedian Adam Hills and London-based nurse Emily Regan.
In honour of the coronation, the Australian government will contribute $10,000 to the West Australian conservation charity Friends of the Western Ground Parrot.
Mr Albanese said King Charles long championed conservation and the government was pleased to mark the event by helping to protect the critically endangered bird.
The King, who is the monarch of 14 overseas realms including Australia, will host a lunch for prime ministers and governors-general at Buckingham Palace and also attend a Commonwealth Heads of Government Meeting on Friday, the day before his crowning.
On Sunday, Australia's Federation Guard will fire a national 21-gun salute from the Parliament House Forecourt, followed by a Royal Australian Air Force flypast.
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