Health Secretary Matt Hancock offered to get vaccinated live on television to help convince people the coronavirus jab is safe.
He stressed that the order in which people received a vaccine would be determined by clinical need.
But said that if a televised inoculation would help persuade people of its safety then that would be "worth it".
Regulators have approved the vaccine developed by Pfizer and BioNTech, paving the way for jabs to start next week.
On ITV's Good Morning Britain, presenter Piers Morgan made the suggestion for a televised injection.
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Morgan said: "I'll come to where you are anytime next week if we can do this. Let's do it together, live on air. It would be powerful, it would send the right message."
Mr Hancock said: "Well, we'd have to get that approved because, of course, there is a prioritisation according to clinical need and, thankfully, as a healthy, middle-aged man, you're not at the top of the prioritisation.
"But if we can get that approved and if people think that's reasonable then I'm up for doing that because once the MHRA has approved a vaccine – they only do that if it is safe.
"And so, if that can help anybody else, persuade anybody else that they should take the vaccine then I think it's worth it."
On Tuesday a senior Tory MP urged Prime Minister Boris Johnson to be at the front of the queue for a vaccine in order to demonstrate its safety.
In the Commons on Tuesday former minister Sir Desmond Swayne also said high-profile celebrities should use their status to support the vaccination drive.
"The way to persuade people to have a vaccine is to line up the entire Government and its ministers and their loved ones and let them take it first, and then get all the luvvies, the icons of popular culture out on the airwaves singing its praises," he said.
But in November, England's deputy chief medical officer Jonathan Van-Tam said it "clearly wasn't right" for people to skip the queue.
Asked whether high-profile Government figures such as himself or the Prime Minister should take a vaccine first to prove to the public it is safe he suggested that the "mum test" – whether you would urge an elderly relation to take it – was important.
"If I could, rightly and morally, be at the very front of the queue, then I would do so because I absolutely trust the judgment of the MHRA on safety and efficacy," he said.
"But that clearly isn't right – we have to target the most highest risk individuals in society and that is how it should be in terms of our system.
"If I could be at the front of the queue, then I would be.
"I think the 'mum test' is very important here.
"My mum is 78, she will be 79 shortly, and I have already said to her – 'Mum, make sure when you are called you are ready, be ready to take this up, this is really important for you because of your age'."