Ministry of Defence chiefs have reportedly been told to come up with plans to ensure the Government can vaccinate those most at risk by mid-February – equating to 13 million people.
Rather than troops, it is believed military planners will be involved in the distribution.
A source yesterday told The Sun: "The Prime Minister is approaching the vaccination roll-out as a military operation and that's what you'll see at tomorrow's press conference."
The Prime Minister will be joined by NHS England chief Sir Simon Stevens and a senior military figure.
Johnson earlier said he expects "tens of millions" of doses to be delivered in the next three months.
But he told the BBC: "I wish I could give you here and now any sort of elaboration on the figures you have already heard about how we hope to get up to two million a week and so on. I can't give you that yet."
NHS sources have also warned the target may be ambitious.
One told the Daily Telegraph: "We do have to manage expectations. You cannot just vaccinate two million people a week from nothing."
GP surgeries in England will on Thursday begin administering the Oxford/AstraZeneca jab.
It comes after the UK reported a further 1,041 people had died within 28 days of testing positive for Covid-19 as of Wednesday, January 6 – the highest daily reported total since April 21.
Record numbers are also currently in hospital with coronavirus, with a further 3,500 admitted in England on Monday, January 4.
The House of Commons, recalled from its Christmas break to vote on the latest lockdown restrictions on Wednesday, voted with a 508 majority for the measures – which could be in place until the end of March.
"After the marathon of last year we are indeed now in a sprint, a race to vaccinate the vulnerable faster than the virus can reach them," the PM told MPs.
"Every needle in every arm makes a difference."