Applications for the scheme to help those fleeing the conflict will open today, but officials said there would be “specific challenges” with the Prime Minister hosting.
Mr Johnson’s official spokesman said it was down to individual ministers whether they chose to give accommodation to a refugee.
“There are specific challenges around security on housing people in No 10,” the spokesman said.
“Various ministers have been asked about this. Obviously it will come down to individual circumstances.
“This is a significant commitment.”
Communities Secretary Michael Gove will set out later the details of a new programme through which people in the UK can offer to host Ukrainian refugees in their homes.
Families will receive a thank you payment of £350 a month and be expected to commit to a minimum of six months of housing an individual or a group.
Transport Secretary Grant Shapps has said he will participate in the scheme.
He tweeted this afternoon:” We've spent the past few weeks as a family discussing the devastating situation in Ukraine, and so we intend to apply today to join other UK households in offering our home to provide refuge to Ukrainians until it is safe for them to return to their country.”
Health Secretary Sajid Javid has said it would be difficult for him to “offer the time” to host refugees, and urged people considering taking part to make sure “that they can fulfil the obligations”.
“I’m starting to have a conversation with my wife on that and I think many households – as you say, and I’m pleased you brought this up – are probably thinking about this across the country,” he told BBC Breakfast this morning.
“It’s important that anyone that becomes a host, that they can fulfil the obligations of a host, that they can spend time with these families and help, but there are many ways that we can all help and whatever I do at a personal level, I will most certainly be helping.”