A boosted payment could support hosts to carry on for more than six months, as energy costs soar amid rising inflation pressures, Refugees Minister Lord Richard Harrington said.
The 'thank you' payment is currently £350 per month.
He is suggesting it should be doubled to £700 a month, due to spiking everyday costs.
Six months on from the start of Russia's invasion, around 25,000 offers of accommodation under the Homes for Ukraine scheme have been taken up, with an average of three Ukrainians living in each home, Lord Harrington added.
The government is now asking existing hosts to extend their generosity and continue supporting Ukrainians, while appealing for new sponsors to step forward.
But as the cost of living crisis deepens and energy bills are expected to soar by 80% going into winter, Lord Harrington has warned more support is needed.
Councils have also issued the stark warning that homelessness could rise if initial six-month placements with hosts end without other options in place.
Lord Harrington said he has been lobbying the Treasury “very hard” to double the payment for sponsors who house refugees for longer than half a year – the minimum period expected of hosts.
“The costs ... they’re paying maybe a big chunk of rent themselves, the mortgage payments have gone up and everything, and I think it’s perfectly reasonable, in my view, to increase the amount that we’re paying them," he said.
More than 115,000 Ukrainians have arrived in the UK under its visa schemes, according to latest government figures, including around 81,700 refugees under the sponsorship scheme.
Around 4,000-5,000 people are arriving each week, Lord Harrington said.
He said the government has emailed everyone who initially expressed an interest in the sponsorship scheme, to see if they are still interested in taking part if they are not already hosting.
He expects roughly 50,000 of the 200,000-plus people who registered their interest initially will go on to be hosts.
In particular, the government wants to recruit extra hosts in areas close to where refugees are currently being sponsored.
This would mean refugees are matched with new hosts nearby so they do not need to leave communities where they have started putting down roots.
“I’m not worried about the shortage of offers; I’m more concerned that they’re in the right area,” he added.
Lord Harrington said his priority is to stop people becoming homeless, and he is hoping to achieve that by encouraging hosts to continue for longer with existing placements, recruiting new sponsors, and enabling refugees to move into the private rented sector.
So far, more than 1,300 Ukrainian single households and families have been assessed as homeless or threatened with homelessness as of July 29.
Lord Harrington said he has met with groups representing landlords to ask if they will waive reference requirements for Ukrainian refugees.
He added that some councils have said they will act as guarantors for those wanting to rent homes, which he is trying to expand.
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Lord Harrington added: “I suspect some of them will need an extra budget to do it, but again, I can argue to the Treasury – it’s my job to say: ‘Well, you actually save money, because people then are not becoming homeless’.”
The minister is also asking for extra funding money for English language lessons, which he said are the “key to employment."
The amount being requested is in the “low tens of millions," he said, adding: “It’s critical. We will get that money back because people get into employment."
Lisa Nandy MP, Labour's Shadow Levelling Up, Housing, and Communities Secretary, said the financial pressures on households could impact the pool of hosts able to offer help to Ukrainan refugees.
"British households across the country have stepped up to help Ukrainian families fleeing this dreadful conflict, but the Conservatives' inaction on the cost of living crisis means thousands could be left out of pocket for opening up their home," she said.
“If the Government do not act now, they will risk a huge number of Ukrainian refugees becoming homeless this winter.
Labour has vowed it would freeze energy bills this winter to ease the energy crisis if the party was in power, saving the typical household £1,000.
The Treasury said the monthly thank you payments for hosts are to “recognise their generosity," and do not affect benefit entitlement nor council tax status.
A spokeswoman said: “We have already acted to make sure these payments are exempt from tax, and continue to monitor and review the support provided under the scheme.”