Lawyers working on behalf of MacKenzie sought an apology from the Force for the ex-editor's "vilification" after he published a story that blamed Liverpool fans for the 1989 disaster.
MacKenzie had claimed that senior officers from South Yorkshire Police were the source of the story, and their claims had persuaded him to pass off the allegations as fact in the paper.
However, South Yorkshire police chief constable David Crompton said that MacKenzie was responsible for the front page article and its inflammatory headline, "The Truth".
The Sun was boycotted in Liverpool after the story was printed shortly after the 1989 disaster. It claimed that there was "mass drunkenness" among fans of the club, who also pick-pocketed the dead and urinated on police.
Published a few weeks ago, the Hillsborough Independent Inquiry report stated that there was no evidence to support the allegations made in the article.
MacKenzie issued a full apology for the article, but that has not stopped people questioning his actions over the headline.
This was particularly after the senior Sun journalist who wrote the article claimed that MacKenzie overrode his objections to "The Truth" headline. Last week, Channel 4 News even confronted MacKenzie at his home, asking for the real truth.
Writing in The Spectator, MacKenzie said that he had suffered "personal vilification for decades" as a result of the article.
He claimed that police patrols have increased around his home, and warned that he faced "physical danger" if he ever went to Liverpool.
But he also said that South Yorkshire Police had got away "scot-free" for "the lies their officers told".
However, Compton said in a statement yesterday that MacKenzie was responsible for the article and headline.
"SYP have received a letter from Kelvin MacKenzie's lawyers which demands the Force makes an apology to him," he said.
"We have publicly apologised to the Hillsborough families and the Liverpool fans but we will not apologise to Mr MacKenzie.
"He chose to write his own headline and he should accept responsibility for it."