Smith wrote to Kraft Foods Inc. on Monday offering to purchase the iconic Australian spread from the global food giant.
"They are looking to sell Life Savers, so they might be interested in selling Vegemite," Smith told reporters.
"Americans think Vegemite is axle grease, they would probably be quite happy to get it off their hands.
"Vegemite is very much an Australian addiction."
Smith said in his letter to Kraft's chief executive officer, Roger Deromedi, that Australians would love to reclaim Vegemite.
According to comments made by Deromedi several months ago, United States-based Kraft is increasingly looking to brands that have global reach and may divest regional brands.
Recent newspaper reports said the company has already given investment bank UBS AG a mandate to offload its Altoids breath mints and Life Savers brands.
Smith said he was aiming to set up a public company with Australian shareholders to buy Vegemite back again.
"I would put in a few million and Mums and Dads could put in a few thousand," he said.
Smith said he was particularly anxious to buy Vegemite given that Kraft was part of the Altria Group, which also owned multinational tobacco company Philip Morris.
"If you're addicted to Vegemite like I am, the money you spend when you buy it goes to US cigarette company Philip Morris, which kills our kids," Smith said.
Smith is well-known for his eponymous food brand, Dick Smith Foods, which sells Australian-owned food and beverage products, in direct competition with foreign-owned equivalents.
Vegemite, a yeast-based spread, was invented in 1922 by Dr Cyril P Callister at the Fred Walker Cheese Company in Melbourne.