Plans to redistribute around 160,000 migrants from Italy, Greece and Hungary to the rest of Europe are due to be unveiled.
European Commission president Jean-Claude Juncker is setting out proposals to share the burden of the influx from across the Mediterranean in a speech.
David Cameron has made clear that the UK will opt out of the quota scheme, as it is not a member of the Schengen borderless zone. But the Prime Minister has been coming under intense pressure to agree to take some of the migrants voluntarily.
In a statement earlier this week, Mr Cameron responded to a wave of public sympathy over photographs of a drowned Syrian child on a Turkish beach by pledging to resettle up to 20,000 people in the UK over five years.
But he insisted they would only be vulnerable refugees from camps in the region around Syria, and not the thousands who have entered Europe by sea and through the Balkans over recent months.
The commitment was condemned by the Archbishop of Canterbury as "very slim”, and Labour and the SNP are demanding the Government does more.
Mr Juncker is expected to argue that the Dublin system, whereby all migrants to the EU must be registered and processed in the country they arrive in, no longer works.
Instead, he is likely to propose a permanent system of mandatory quotas for migrants that would be triggered by large influxes.
Countries would take a proportion of those arriving based on their size, economic health and the number of refugees they had already accepted.