The government is reportedly aiming to reduce the gap between vaccine doses from eight to four weeks.
With the threat from the Delta variant along with the easing of restrictions, ministers are keen to see the vaccine rollout sped up.
It comes as the latest figures from Public Health England show cases of the dominant Delta variant rose by a third in the past week.
A total of 216,249 confirmed and probable cases of that variant, first identified in India and which now accounts for approximately 99% of confirmed cases of coronavirus across the UK.
The majority of people being admitted to hospital in England with the Delta variant are unvaccinated, according to the PHE figures.
The Joint Committee on Vaccination and Immunisation have been asked to approve the quicker time scale for jabs, reports The Sunday Times.
A No 10 source told the newspaper the committee has been asked to provide urgent advice on the pros and cons of reducing the gap between doses to four weeks.
If given the go-ahead it would also allow many more people to travel abroad this summer and avoid quarantining - which is to be made possible for people with both doses.
Prime Minister Boris Johnson is expected to confirm on Monday that a final easing of coronavirus restrictions will take place in England on July 19.
The government has said it will have offered all adults in England a first dose by July 19.
Around 86% of adults in England are estimated to have received one dose of Covid-19 vaccine, with around 65% having had both doses.
Vaccine take-up varies between different age groups, with more than 95% of people aged 50-79 estimated to have had one dose.
Among younger groups, 88% of 40-49 year-olds are likely to have had one dose, along with 78% of 30-39 year-olds and 60% of 18-29 year-olds.
Chris Hopson, the chief executive of NHS Providers, said: “We’ve had a significant number of trust chief executives this week saying they are very worried about the number of unvaccinated young people who are getting Covid, showing mild symptoms but then coming back relatively soon with much more serious long-term symptoms.
"Trust leaders are worried we might look back in six or nine months’ time and say rapid, full relaxation of the restrictions was a mistake, because if we’d waited a few weeks longer, we would have a lot more younger people double-vaccinated.”
Health authorities have told vaccine centres to follow the guidance stating nobody should receive their second dose less than eight weeks after their first jab, with PHE saying “there is evidence of better immune response and/or protection where longer intervals between doses are used”
The government is pushing for more young men in particular to get vaccinated.
There has been a general fall in demand for vaccines, and nearly half of males from 18 to 24 have not received a dose, three weeks after it became available to them.
A publicity campaign is being planned to encourage youngsters that could include the England team and influencers.
Fans attending England's Euro 2020 final against Italy have been urged to use the opportunity to get a Covid jab at the Wembley vaccination centre.
The concern is that young males are also the group which have had the highest number of infections with 41,462, having tested positive in the past fortnight, according to Public Health England.
There is a concern that long Covid cases could reach very high numbers if infections continue to rise.
