Sajid Javid said any such move would ensure patient safety due to hospitals being “full of vulnerable people”.
Speaking during a visit to Moorfields Eye Hospital, Mr Javid said: “It’s right that we do everything we can to protect the most vulnerable from this virus, that is why we have already insisted that those staff that work in care homes get vaccinated and I think people know why that’s so important.
“The reason we have launched this consultation today for the health sector, for the NHS is because obviously hospitals are full of vulnerable people and I think it’s our duty to make sure that we are considering this.
“We haven’t made a decision but we do want to listen to what people have to say because I think it is important that we show that patient safety will always be a priority.”
It came after care minister Helen Whately said those who refuse to be inoculated against Covid-19 could be moved to back-office roles.
The six-week consultation will determine whether vaccination will become a condition of deployment for frontline workers in health and care settings.
It means staff could be required to have both Covid and flu vaccines to protect patients from infection, serious illness or death.
Ms Whately told Times Radio that while there were people who could not have the Covid-19 vaccine for medical reasons those who decline the jab could lose their frontline jobs.
She said: “You can look at whether there are alternative ways somebody could be deployed, for instance, in a role that doesn’t involve frontline work, or doesn’t involve being physically in the same setting as the patient, whether it’s, for instance, working on 111, something like that.
“So we could look at alternative roles for individuals, these are exactly the sorts of things that we can investigate.”
Some 92% of NHS staff have had their first dose of a coronavirus jab while 88% have had both doses.
Figures published by NHS England on Thursday suggest that 233,181 social care staff, outside of those working in older age care homes, are yet to be vaccinated.
Some 82.7% of staff working in care homes for younger adults, or in domiciliary care, have had a first jab, as have 74.9% of those working in other settings, such as non-registered providers and those employed by local authorities.
Some 88,500 (17.3%) staff working in care homes for younger adults, or in domiciliary care, have not yet had a first jab or their first jab has not yet been reported.
The same applies to 144,681 staff (25.1%) working in other settings, such as non-registered providers and those employed by local authorities.
Workers in registered care homes have already been told they will need to be double jabbed as a condition of deployment in England’s care homes by November 11, unless they are exempt.
Asked by the BBC whether unvaccinated staff should be sacked, Ms Whately said they could be deployed to alternative roles, adding: “This is really difficult, but I don’t know about you, I’ve certainly spoken to people receiving care in care homes, or the families of those in care homes, and they want their family members to be looked after by people who are doubly vaccinated.
“They want their family members to have the most possible protection against this horrible disease.”
It comes as leading experts from the Joint Committee on Vaccination and Immunisation (JCVI) meet to discuss who should get booster jabs this autumn, with a final decision expected before the end of the week.
Mr Javid said on Wednesday that updated JCVI advice on the issue is expected in the next few days.
Speaking on BBC Radio 4’s Today programme, Professor Adam Finn, from the JCVI and the University of Bristol, said it would be better to persuade people of the vaccine’s benefits rather than make them compulsory for health workers.
He said making jabs compulsory was “kind of an admission of failure”, adding: “It’s like saying you can’t either find the time or find the ability to explain to people why it makes sense and create the culture in which everybody does it because they understand why it’s important.
“If you build a culture, it becomes the norm and everybody does it.”
But he added that he understood why it was being considered.
“We are in a pandemic and so things sometimes get done differently,” he said.
Unison head of health Sara Gorton said: “The key to convincing hesitant staff is persuasionâ, not force. Pushing NHS staff to get vaccinated âwill create resentment, destroy âalready fragile morale and âreduce take-up.
“âOf course, everyone who can should be jabbed, but as with care, compulsion is not the way.”