The Sun reports that family doctors may have the capacity to offer the vaccine seven days a week between 8 a.m. and 8 p.m.
It is believed that major cities will also have a Covid-19 vaccination center to help speed up vaccine distribution.
General practitioners could be supported by 3,000 mobile units, teams going to care homes and vulnerable people, the newspaper reported.
It comes after Pulse Today, a magazine for generalists, said a Covid-19 vaccine could be given to more than 85 people and frontline NHS workers next month.
The publication reported that surgeries will be urged to prepare to administer the vaccine from early December.
Pulse reported last month that the NHS was looking to start the vaccine rollout from December, with sources familiar with the problem putting the odds at “50/50”.
According to the latest data, the UK has recorded 355 new coronavirus-related deaths and 23,287 new cases.
The Office for National Statistics said that in England, around 618,700 people – one in 90 – had Covid-19 between October 25 and 31, compared to 568,100 the week before.
But while the infection rate has increased in recent weeks, “the rate of increase is less pronounced compared to previous weeks,” the ONS said.
Health chiefs say the UK will have 10 million doses of the vaccine by the end of the year.
Richard Vautrey, chairman of the British Medical Association’s GP committee, said Christmas jabs were a possibility.