From the National Archives, here's a letter by Thomas Jefferson discussing monetary policy.
This is an explicit explanation of his views on the economic merits of the question, not simply the constitutional question of whether the federal government can charter a national bank (an argument with which I presume the readership of this blog is familiar).
Jefferson is an "elder statesman" when he writes this letter, in November 1813. He hasn't been President for more than four years. Further, the original "Bank of the United States," the one that Hamilton created over Jefferson's strident objections, is no longer in operation. Its charter had expired and gone unrenewed during Madison's first term.
BUT ... it was proving difficult to finance the ongoing war without a central bank, and this caused some soul-searching within the Republican-Democratic Party, by now the only national political party left. Hence the discussion. Eventually the party would split over this issue, with the Whigs supporting a new Bank going their own way (and uniting in the process with the remnants of the Federalists). But that's in the future.
The letter may be considered part of the war-financing-inspired soul searching.
Jefferson's own view it seems is that the optimal situation is for "specie" (precious metals) to serve not only as the backing of money but AS money, as the chief circulating medium. He acknowledges Adam Smith's view that circulating money (paper notes BACKED by specie) can be a valuable corollary, but he is very wary about that. It sounds too Hamiltonian to him.
Let's just call this post my contribution to Throwback Thursday.