The Sunday Mail claimed the AFL had told the Power there would be "no more welfare" after the end of the club's three-year $9 million rescue package.
The report said Demetriou told the club, "You can't come back for another lick".
Speaking at a function ahead of the clash between the Power and Western Bulldogs at AAMI Stadium on Sunday, Demetriou said the quote was inaccurate.
"I've never used the quote in the article, 'Don't come back for another lick'," Demetriou said.
"It's just absurd. It's wrong and he should retract that in tomorrow's newspaper. It's complete and utter crap."
The newspaper report said the Power had been warned they wouldn't receive any more welfare from the League if they failed to turn around their finances around ahead of the move to the Adelaide Oval in 2014 or 2015.
"The journalist never rang me for a comment and I think it's incumbent upon all journalists that if you're going to write an article like that you should actually go to the source to verify information," Demetriou said.
The AFL chief, in Adelaide ahead of an AFL Commission meeting with the SANFL, Crows and Power on Monday, also dismissed speculation Port Adelaide could be rebranded or cease to exist at the end of the current broadcast rights agreement in 2015.
"We need two teams in South Australia and I can't imagine having another club other than Port Adelaide and the Adelaide Crows," he said.
"The stories that are going around that we can just put in another team [in place of Port Adelaide] as long as there are nine games, that's crap too.
"We've actually said ad nauseam with the support of the SANFL and the support of the Crows, that we want two teams in South Australia.
"To do that you've got to have two teams - one is Adelaide and one is Port Adelaide.
"There's no new team coming in and no games being bought out of Melbourne to be played here … so please, can people stop speculating and commenting about things they know nothing about."
The renewed speculation over Port Adelaide's future was the latest in a long line of controversies for the club this season.
Demetriou conceded the Power, who have won only two matches and are poised to secure their first-ever wooden spoon, couldn't "get any lower" but called for an end to the negativity surrounding the club's on and off-field fortunes.
"This club's got to build slowly. It won't be easy and it'll be painful at times … but football club supporters are very passionate and have got to support football clubs through thick and thin," he said.
"The Port Adelaide Football Club is probably in better shape than the Melbourne Football Club was three years ago when Jim Stynes volunteered to get involved, wiped out $5 million of debt … and set about putting the club back on the path to rebuilding.
"It was the same with the Western Bulldogs a few years ago."
"To rebuild the Port Adelaide Football Club is going to take a long time. It's a multi-faceted attack, but it's been done before."
