Health Secretary Sajid Javid said he is “having conversations” with his wife about taking in Ukrainian refugees.
Tens of thousands of people forced to flee Vladimir Putin’s war could come to the UK under a Government scheme which allows people to offer a room to a refugee.
Households in the UK will be offered a £350 a month “thank you” payment to open their homes to those fleeing under the new sponsorship programme.
Mr Javid told the BBC he was considering whether he was able to host Ukrainian refugees in his own home.
He said: “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.
“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.”
He added that the Ukraine Family Scheme for refugees was "being made easier and more straightforward" from Tuesday following criticism that visas were taking too long to process for those fleeing war.
Just over 3,000 visas have now been granted through the programme. The UK has pledged to take in more than 200,000 refugees.
Fellow cabinet minister Michael Gove has also said he was also willing to house someone from Ukraine.
The Levelling Up Secretary set out details of the new sponsorship route on Sunday.
Asked on the Sunday whether he would take in a Ukrainian refugee, Mr Gove said: “Yes.”
He added: “I’m exploring what I can do, I know that there are others who have. Without going into my personal circumstances, there are a couple of things I need to sort out - but, yes.”
London mayor Sadiq Khan said London is ready to take in “thousands and thousands” of refugees, but Government funding was needed to make sure they get the help they need.
“We know almost half of those with links to Ukraine live in London,” he told BBC Radio 4.
“We also know from our experience last year we are able to quickly house more than 3,000 arrivals from a Afghanistan. We have had over the last few days and weeks a large number of offers from councils, we have been coordinating hotels .
“We also know Londoners, and I have got nothing but admiration for them, are happy to host those from Ukraine.
“We think we could take thousands and thousands of those who are fleeing Ukraine in our city with the combination of the generosity of Londoners, councils, hotels, those in the private sector. But the stumbling block is the lack of certainty with the delays in the visa system, which is leading to many Londoners and businesses being ready to step up but not knowing when they are going to arrive. Also we need some support from the Government.
“Those who arrive will need wraparound support. Think about the trauma people have suffered.”