Krasner said after a specially convened board meeting at Elland Road that none of a number of interested parties had met necessary conditions.
Sainsbury, the 41-year-old great- grandson of the British supermarket founder, earlier said he was heading an Anglo-American group's interest.
And he warned the club's board they faced the stark choice of accepting the £25m deal or losing their ownership of Elland Road.
However, Krasner said in a statement: "The board of Leeds United confirms a number of discussions are continuing with various parties, and at this stage no agreement has been signed.
"We have always insisted any interested party must be able to confirm the necessary funds are available to complete any transaction. Despite much press speculation, as we stand, no party has met our conditions."
Leeds have significantly reduced their debt under Krasner. But having off-loaded their star names and agreed a lease-back deal on their Thorp Arch training complex, only Elland Road remained.
Sainsbury said the primary intentions of his group were to buy back Thorp Arch, secure the future of Elland Road and provide manager Kevin Blackwell with cash to spend.
Sainsbury said: "The board has two options - the option we have put forward or the option of selling Elland Road, the pride and joy of Leeds United for the past 85 years.
"They have to make a decision which is in the best interests of the shareholders, the players and particularly the fans, and I know which way I would go."
Sainsbury, who boasts business interests including restaurants and a London bar, has been involved in negotiations for three months.
But the main man behind the bid is Tampa Bay resident Burl Sheppard, a telecommunications executive whose motives, not to mention his business history, remain shadowy.
Sheppard has been linked with many now-defunct companies and is unknown to media outlets in Florida.
And Sainsbury has conceded that the Nova financial group named as backing the takeover is merely an investment vehicle for the interested individual parties.
That will not encourage Leeds fans who are weary of takeover talk as the club continues to struggle at the lower end of the Championship table.
Sainsbury insisted that if his bid was successful he would work hard to get the fans back on side.
"I want to work closely with the supporters with the objective first of getting back into the Premiership. Then we must re-establish Leeds as a top club. When I was 12 years old and lived in London everybody knew who Leeds were. This is not going to a Malcolm Glazer-type story or a Russian revolution.
"I want to be straight and avoid disappointing people. I want to communicate with the players and supporters and to work out the next move together."
But Sainsbury may already be having regrets about fronting a bid which already appears less than secure.
He admits to being taken aback by the level of interest in his first foray into the football world.
Sainsbury added: "This has opened my eyes to how much football means and it is quite a scary prospect. I am not somebody who walks around with body guards or public relations officers and it is a scary thought that I will have a public profile.
"But this is one of greatest names in English football and anybody would relish the challenge of realising their enormous potential."