Cameron has previously said taking more refugees wasn’t the answer to Europe's migrant crisis, however PoliticsHome reports that he has now said Britain will take in “thousands” more people.
The extra numbers are expected to come from refugee camps from around Syria, rather than from people who have already made the journey to an EU member state.
Cameron is expected to make an announcement after meeting with the Spanish and Italian prime ministers on Friday.
This follows mounting pressure for the UK to accept more refugees as the crisis spread across the EU this week.
Former UK minister David Blunkett said the UK should take in 25,000 refugees over the next six months.
The UN's special representative on migration, Peter Sutherland, said certain countries were "massively bearing the burden", but the UK and others "can do more" to alleviate the situation.
The interim leader of the UK socialists (Labour Party), Harriet Harman yesterday called on Cameron to press for an emergency EU summit.
Andy Burnham, the Labour Party Shadow Health Secretary, claimed the UK response had "veered from inadequate to misjudged" and was "a stain on our nation's conscience".
He called for an emergency debate on the issue when British MPs return to work next week.
The leader of the UK Liberal Democrats Tim Farron echoed the calls for an urgent debate to take place when the British Parliament reconvenes on Monday.
"We can and must do more with our EU partners to tackle the problem. This is a humanitarian crisis which shames our country. We must step up to the plate to tackle it,” he said in a statement.