The BBC reports that the extra refugees are expected to come from UN camps bordering Syria, and not from among people already in Europe.
No specific figure has been agreed, but Mr Cameron has previously said the UK would continue to take in "thousands".
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.
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, Alan Kurdi, 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 in25,000 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 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.