The Sunday Herald understands that the Edinburgh-born businessman, who made an offer to buy Rangers earlier this year before joining forces with the Blue Knights consortium, has no intention of looking into the Tynecastle club's situation.
The owner of Sale Sharks rugby club, Kennedy attended Tynecastle High School but grew up as a Hibernian supporter. He was keen to try to bring Rangers out of administration, but will not seek to help Hearts as they try to find the means to pay a £450,000 tax bill, with a further £1.75m bill is under appeal.
Kennedy was quoted last week as saying, "you never know", but he will not become involved, even though the Hearts director, Sergejus Fedotovas, said last Friday that the Tynecastle board will reach out to the multi-millionaire.
"We definitely need to contact him," Fedotovas said. "We can't afford to waste any opportunity. We will have a goodwill discussion with anyone who has a reasonably opportunity to take over the club."
Meanwhile, Dunfermline Athletic chairman John Yorkston insists they will be able to pay a November tax bill on time and so ensure the club does not go into administration.
They must pay £50,000 by November 19, with a further £31,000 two days later, and rumours were rife following boardroom reshuffles that the club was verging on insolvency.
"We've been there before and got through it and intend to get through it again," said Yorkston. "Enough folk have said they will help and if it all comes in, we should be fine. We have a famine in November, but a feast in December and early January, with two derbies and a share of the Scottish Cup income from the match against Partick Thistle."