Sainsbury said Nova Financial Partners had begun to provide proof of funding for a bid reportedly worth £25million, reports the BBC.
"The consortium has produced the first of a number of documents showing that we have the funds in place to complete the transaction," he said.
Leeds had insisted they were still some way from concluding any takeover deal.
But Sainsbury - the great grandson of the founder of the supermarket chain - believes he will have control of the club by the middle of next week.
"We appreciate the efforts that the board has gone to in extending the time in which to make available to them our proof of funding," the businessman said in a statement.
But chairman Gerald Krasner continues to exercise caution, having seen a number of deadlines expire amid mounting concerns that the deal could fall through.
And waiting in the wings is Yorkshire property tycoon Norman Stubbs, a Leeds supporter who has held his own negotiations with the board regarding his own takeover.
