The club's board demanded evidence of funds after considering the offer.
But Sainsbury told BBC Radio Five Live: "We are the right people to take over. We will deliver proof of funds.
"I'd like to deliver proof of funds on Friday but more realistically it will be on Monday. We still have a team in Leeds sitting there to do a deal."
Sainsbury, who heads the consortium behind the deal, claims that Leeds have reneged on promises that had been agreed earlier in the week.
"On Tuesday we made a formal approach to buy Leeds and we agreed terms and conditions," he added.
"It seems like the conditions of the deal have now changed."
"They said (it was because) of proof of funds but they were offered a £500,000 non-refundable deposit on Wednesday. If that money didn't arrive they could tear up any agreement we had."
Sainsbury's bid would see the club buy back their Thorp Arch training base and secure the future of Elland Road.
Leeds chairman Gerald Krasner said in a statement that discussions were continuing with various parties but no agreement had yet been signed.
"We have always insisted that any interested party must be able to confirm that the necessary funds are available in order to complete any transaction.
"Despite much press speculation, as we stand now, no party has met our conditions," added Krasner.
Sainsbury confirmed that he remained committed to the takeover and believes that his consortium is the right group to take over the club.
He added that of the proposed £25million, £2million would go into shares with the remainder going to pay off the estimated £17million debt, leaving manager Kevin Blackwell with around £5million for new players.
