According to the newspaper, it would be the first time the UK has exported vaccines to the EU amid tensions over delayed deliveries of AstraZeneca shots to the bloc.
A cabinet minister described the plan as a "poke in the eye for Brussels," which has coordinated vaccine procurement and deliveries on behalf of member states.
The UK is said to be seeking to help Ireland to avoid getting a coronavirus hotspot at its borders and more safely lift the lockdown in Northern Ireland.
"Everyone can see the logic of it. It’s good politics while at the same time solving a genuine public health concern in Northern Ireland," a cabinet source said.
The source added that "Easter will be when we might be able to start offering vaccines to Ireland."
The government, however, is also mulling plans to share surplus vaccines with other EU nations over fears that "the poor vaccine programme in France and Germany" could bolster extremist parties.
"The fear is that [French President Emmanuel] Macron has made such a mess of things that it might mean we end up with [leader of the right-wing National Rally party] Marine Le Pen getting elected. No one wants that," another Whitehall source said.
Nearly 30 million Britons have received at least one dose of a coronavirus vaccine. Of them, 3.2 million have been fully vaccinated. The immunization in the EU is progressing slower due to vaccine delivery delays.