The policy requiring National Health Service employees and social care workers to be fully vaccinated by April 1 was announced in November.
It would require all staff to receive their first shot later this week to meet that deadline.
The policy has met resistance from some workers, with warnings that sacking those who did not comply could leave the NHS facing significant staff shortages, while a number of MPs in Prime Minister Boris Johnson's Conservative party have also criticised the decision.
The Daily Telegraph has reported that mandatory vaccination would be dropped and an update from health minister Sajid Javid is due later on Monday.
Treasury Minister Simon Clarke earlier said the government was prepared to look again at the policy in light of the emergence of the Omicron variant of COVID-19, which is more transmissible but results in milder symptoms.
"We do recognise those realities and that does open a space where we can look at this again," minister Simon Clarke told Sky News.
More than 156,000 people across the UK have died in the pandemic.
But the backlash against mandatory vaccination is in line with wider sentiment across the world as people from the United States to Ukraine argue that such rules violate human rights and civil liberties.
However, governments say vaccinations are crucial to contain the spread and reducing severity of the infections, and thereby cut down cases that need to be hospitalised.
