Discussions are under way between pharmacists, vaccine makers and the Government after cases of coronavirus surged this winter.
Latest figures showed there were an average of 3,631 people in hospital with Covid every day during the seven-day run to Christmas.
That was up 12% from the week before, and 57% month on month.
In England and Scotland, about 2.5 million people were thought to be suffering with coronavirus on December 13 – or one in 24.
This is about double the number of people who had it at the start of December.
This winter the Government restricted the number of people eligible for a Covid jab, with only those aged 65-plus offered the vaccine, along with NHS frontline workers and the clinically vulnerable.
The Government previously banned the purchase of Covid vaccines privately over fears it would not have enough to inoculate the most vulnerable.
But health minister Maria Caulfield has now said the Government supports manufacturers and pharmacists that want to set up a private offering.
Pharmacies would offer the vaccines to paying customers in the same way as the flu jab, which costs between £10 and £20 for those who do not qualify for a free dose.
However, it is not known how much a private Covid jab could cost.
In the US, Pfizer indicated it could charge up to £102 for one adult dose.
This is much higher than the £15 per dose the US government paid when the world was preparing for the mass vaccine rollout.
In the UK, each dose is thought to cost the NHS around £10.
A spokesperson for Superdrug, which currently offers the flu jab for as little as £8.79, said it is “in discussions with suppliers about potentially offering a private Covid vaccination service in 2024”.
Boots also said it would like to offer the vaccine.
A Pfizer spokeswoman said: “We are currently exploring the potential of providing Covid-19 vaccines privately in the UK.”
