The German is joining the Racing Point team next year, which will re-brand itself as Aston Martin in the wake of owner Lawrence Stroll's takeover of the British carmaker.
A few days ago, Mercedes team boss Toto Wolff - who has been closely aligned with Stroll in recent times - indicated that Vettel might follow his lead by buying some shares in Aston Martin.
"First and foremost, Sebastian is a racing driver," he said. "But that doesn't mean that he might not buy a few shares as well - especially if the company is still valued low."
Vettel confirmed at the Nurburgring: "I think everyone is free to do what they want with their money.
"Aston Martin is a public company so anyone can invest in it. If you ask me if I have shares, then I will answer that I do.
"How many? That is a question that I do not want to talk about. But I believe in the project - I signed a contract with them.
"I'm looking forward to finding out what we can achieve together next year," he added.
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