Health Secretary Matt Hancock revealed on Tuesday that plans were being considered to make the vaccine mandatory for those working in homes.
Earlier this week, the Government confirmed it is considering the possibility of making vaccination a legal requirement for care home staff.
The Telegraph reported details of a leaked paper submitted to the "Covid O" sub-committee of Cabinet, which said the Prime Minister and the Health Secretary had agreed to the proposal.
Matt Hancock has insisted "no final decision" has yet been taken, but pointed to doctors having to have the hepatitis B vaccine as a condition of employment.
The plans have emerged amid concerns of low uptake of staff in care homes looking after those who are among the most vulnerable to the virus.
Some one in five care staff (21 per cent) in Yorkshire and the North East have not taken the vaccine, according to latest figures.
The figures are higher in Leeds with 31 per cent of staff not taking the vaccine.
Mike Padgham, chair of the Independent Care Group and owner of St Cecilia's care home in Scarborough, warned against making the vaccine mandatory.
He said: "It has to be the choice of the person. If you are already in a job in a care home environment, that's difficult in terms of employment law. It's different if you're looking for a job in care.
"It's not so difficult to say 'if you want to work in this industry, you've got to have the vaccine.' If you are going to make it compulsory in care homes, surely it should be compulsory in the NHS as well.
"I don't think you can force people to have it. It's a balanced risk. Perhaps people who haven't taken it should have tests every day to prove they're negative, there are other things we can do.
"There can be health reasons, cultural reasons or religious reasons - it's a difficult one and we could get into discrimination happening."
Trade union UNISON said proposed mandatory vaccines "smack of a bygone age or of authoritarian regimes".
General secretary Christina McAnea said: "Everyone wants the pandemic over and vaccinations are the route to normality, but turning the clock back to Victorian times by forcing care workers to be jabbed isn’t the way.
“All those who can have the vaccine should. But the key to getting the numbers up is for employers, unions and the government to work together.
“Instead of leaping to the law, ministers could start by putting the funds behind a targeted advertising campaign aimed at care staff."
She added: “Nervous staff need extra time. They must be encouraged to talk to colleagues who’ve had their jab and be persuaded there's nothing to fear."
Nadra Ahmed, chairman of The National Care Association, which represents care providers, said "cultural reasons" were among the factors behind some care home workers not taking up the vaccine.
She also said anti-vax campaigns along with concerns raised over the AstraZeneca vaccine had not helped the cause.
She said: "We support the view that all care home staff should take up the option of the vaccine, however to make it compulsory at this moment in time might not be the right way forward.
"We should be ensuring they have access to the vaccinations, and all the information they want, so they can make an informed choice."