David Cameron is expected to announce plans later to increase the number of refugees being allowed into the UK.
No specific figure has been agreed, but Mr Cameron has previously said the UK would continue to take in "thousands".
The extra refugees are expected to come from UN camps bordering Syria, and not from among people already in Europe.
The PM, who has faced growing pressure to do more to address the crisis, is likely to make an announcement in Spain after talks with fellow leaders.
He is meeting his Portuguese and Spanish counterparts for talks that had been intended to focus on his desire for EU reform, but which will be overshadowed by the migrant crisis.
'Deeply moved'
Calls for the UK to take in more refugees have intensified after the publication of a picture of the body of a drowned three-year-old Syrian boy washed up a Turkish beach.
Mr Cameron said on Thursday that as a father he felt "deeply moved" by the image, but has argued that taking on more people was not the simple answer.
- But it now appears that his stance is shifting amid pressure from public and political figures, including:
Scottish First Minister Nicola Sturgeon has written to Mr Cameron calling for the UK to accept more refugees
Former Labour Home Secretary David Blunkett said the UK should take in 25,000 over the next six months
A petition calling on the UK to accept more refugees has got more than three times the 100,000 signatures needed for it to be eligible for a possible debate in Parliament
Meanwhile, a tense stand-off between police and migrants on a train in Hungary is continuing into a second day.
On Thursday, police let the migrants board the train in Budapest but then tried to force them off at a refugee camp to the west of the capital.
Since 2014, the UK has accepted 216 Syrian refugees under a scheme to relocate the most vulnerable, and almost 5,000 Syrians have been granted asylum in the last four years.
Among those to add his voice to calls for the UK to do more is Chief Rabbi Lord Sacks, who told BBC Newsnight that the UK needed to make "a very clear and conspicuous humanitarian gesture".
"I think 10,000 is a figure that we could handle," he said.
"It's a figure to which Britain would respond - the churches, the religious groups, the charities, would all join in, local civic groups.
"And I think we'd be better for doing that."
Development charity Oxfam welcomed indications of a shift in UK government policy.
Chief executive Mark Goldring said: "Offering to resettle 10,000 Syrian refugees would bring the UK in line with other European countries who have already shown leadership in offering a haven to vulnerable refugees."
Credit: The BBC
