An earlier source is the 1889 History of the United States of America during the first administration of Thomas Jefferson Vol. 1:
Ages must probably pass before the interior could be thoroughly settled ; even Jefferson, usually a sanguine man, talked of a thousand years with acquiescence, and in his first Inaugural Address, at a time when the Mississippi River formed the Western boundary, spoke of the country as having "room enough for enough for our descendants to the hundredth and thousandth generation".
So a true quote is from His First Inaugural Address:
Let us, then, with courage and confidence, pursue our own federal and republican principles our attachment to union and representative government. Kindly separated by nature and a wide ocean from the exterminating havoc of one-quarter of the globe; too high-minded to endure the degradations of the others; possessing a chosen country, with room enough for our descendants to the hundredth and thousandth generation; entertaining a due sense of our equal right to the use of our own faculties, to the acquisitions of our own industry, to honor and confidence from our fellow citizens, resulting not from birth, but from our actions and their sense of them; enlightened by a benign religion, professed, indeed, and practised in various forms, yet all of them inculcating honesty, truth, temperance, gratitude, and the love of man, acknowledging and adoring an overruling providence, which by all its dispensations, proves that it delights in the happiness of man here and his greater happiness hereafter; with all these blessings, what more is necessary to make us a happy and a prosperous people?
The 1911 book A History of the Northern Peninsula of Michigan and Its People claims that "as late as 1790" Jefferson said:
not in a thousand years will the country be thoroughly settled as far west as the Mississippi
The 1892 article Jefferson's Prophecy One Century Ago in The Magazine of History with Notes and Queries, Volume 28, has the statement:
Jefferson predicted that it would be a thousand years before the country would be thickly populated as far west as the Mississippi
and cites to "Professor Hart's Epochs of American History" which has the identical statement, and gives an extensive list of references at the beginning of the chapter.