Police officers and teachers could be given priority in the next phase of the vaccine rollout.
Hundreds of thousands of shop workers could also be added to the list, UK Vaccines Minister Nadhim Zahawi has hinted.
He has said they are looking at jobs that come into close contact with the public as a result of their jobs and if they should be considered for priority access.
The decision across the whole of the UK on who will get the jab and when will be taken by the Joint Committee on Vaccination and Immunisation (JCVI).
UK Health Secretary Matt Hancock has called for a national debate on prioritisation.
Wales' coronavirus vaccine strategy, which was published last week, sets three key milestones. See the key dates in Wales.
The first is for all care home residents and staff, frontline health and social care staff, everyone over 70 and everyone who is clinically extremely vulnerable to be offered vaccination by mid-February.
This is in line with the target set by the UK Government to inoculate the first four priority groups. In Wales that equates to around 700,000 people. To date, 150,000 have been given a vaccine, meaning there is still a long way to go.
"If we can vaccinate this group, it would protect the people most at risk of serious illness and harm if they catch coronavirus," said Health Minister Vaughan Gething.
The JCVI is now deciding who should be top of the list in phase two.
Talks on how schools can re-open safely, and when, are ongoing with the Welsh Government, local authorities and unions.
One of the key issues is whether staff should be prioritised for the coronavirus vaccine after the elderly, vulnerable, health and care workers.
Mr Zahawi told Times Radio: "Teachers, police officers, shop workers, those who through no fault of their own, other than the work that they do, may come into contact with the virus at much greater volume [should be] the top of the list.’
It is not known whether Mr Zahawi was referring to all shop workers or just those working at the height of lockdown in supermarkets and corner shops.
Speaking at the Downing Street press conference on Monday, Mr Hancock outlined how a decision on vaccine priorities would be made.
He said: "The clinical advice is to go through the top groups... and then after that it is essentially about protecting people as well as possible according to a judgment about who should come next.
"That is why we should have a debate about that.
"Ninety-nine per cent of deaths occur in the top nine groups and after that it is about protecting against transmission and getting life back to normal as soon as possible.’"
Cabinet ministers such as Mr Hancock and Home Secretary Priti Patel have previously said police officers and teachers have a good case for being placed at the top of phase two of the rollout.
Public Health Wales data also shows 151,737 people have now received a first dose of the coronavirus vaccine as of 10pm on Sunday (January 17), up 25,362 on the figure last published on Friday. There are 201 people who have received both of their vaccine jabs. Latest figures here.
Last week, a teaching union leader in Wales warned that schools cannot re-open as they were last term, let alone as they were before Covid, until all staff are vaccinated.
Welsh Government minister Kirsty Williams has said that she would follow the guidance from the UK-wide JCVI body.
"I fully stand behind the work of the JCVI in how it has identified who is most at risk of serious harm or death as a result of contracting Covid-19," Ms Williams told the Senedd last week.
"Members of staff, both in school and those that support education in other roles, will receive their vaccination in line with their relative risk of harm."