A letter from the Chelsea and Westminster Hospital Foundation Trust in London to staff reportedly says: "We will be making Covid vaccination mandatory for all our employees and it will form part of the employment contract."
The letter- which The Independent has seen a copy of - reports the document is signed by the trust's chief executive Lesley Watts.
Six thousand staff who have "chosen" not to be vaccinated are being called on to change their minds.
The letter reportedly states: "We will need to take into account your vaccination status in your occupational risk assessment and this may impact the range of duties you undertake and indeed the environment in which you work."
The letter has also reportedly been sent to other NHS bosses in London with the suggestion that they "adapt and use" it in their trusts.
It is believed that adding vaccination requirement into employment contracts would amount to a change in terms and conditions for staff that could throw up legal challenges.
The Chelsea and Westminster Hospital Foundation Trust and NHS England have been approached for comment.
Vaccines may be made compulsory for certain key workers if they want to keep their jobs.
Health Secretary Matt Hancock today appeared to confirm that the Government will try to make vaccination compulsory for those working in elderly care homes.
He said staff have a "duty of care" to get themselves vaccinated because elderly residents are the ones most at risk of dying from the virus.
Mr Hancock said industry bosses were united in their calls for a "no jab, no job" policy, insisting good uptake was "our route out of this pandemic", according to MailOnline.
Worried scientists claimed lockdown lifting could be put into reverse due to the “very concerning” South African variant.
A large cluster of the mutant strain has been reported in London, where some residents have been urged to get a test immediately.
Prof Peter Openshaw, a member of a Sage group - the Covid-19 clinical information network - told BBC2's Newsnight: "A lot of we scientists are very concerned about what's happening at the moment.
"I think we're all just hoping that the staged reduction in lockdown is going to be OK. It is being done reasonably cautiously but I think this is not good news.
"If we get rapid spread of the South African or other more resistant variants, it may well be that we are going to have to put the reductions of lockdown into reverse."