Pret A Manger's owner Bridgepoint is considering selling the sandwich chain or floating it on the New York Stock Exchange.
"All options are open," Jackson told the Financial Times, which reports he did not rule out a sale rather than an initial public offering (IPO). The group would be expected to see a seven-fold return on its initial investment should it be sold.
Jackson added: "We've thought that the best route for Pret in the long term is to be a quoted company. We'd love to be able to do that in the United Kingdom and that's been on our mind," however flotation in the US would support the company's US expansion ambitions.
Pret has more than 500 stores worldwide, at least 329 in the UK and 74 in the US, since opening its first site in London's Hampstead in 1984. Pret saw sales grow 15% to £776.2m, driven by sales in dairy- and gluten-free ranges, in its last set of financial results.
Pret A Manger declined to comment.