The European Commission will make the controversial proposal that EU member countries should take in refugees under an EU quota scheme.
The UN estimates that 60,000 people have already tried to cross the Mediterranean this year.
Migrants are being driven to make the journey by “horrific abuse” in Libya, according to Amnesty International.
More than 1,800 migrants have died this year in the Mediterranean, a 20-fold increase on the same period in 2014.
The European Commission’s migration policy, to be announced on Wednesday, will also propose organising legal means for migrants to come to Europe so they do not turn to traffickers.
However, it will need to be agreed by EU states.
European leaders will discuss the proposals at a summit at the end of June.
Approval of the proposals is unlikely to be straightforward as the UK is strongly opposed to the idea, reports the BBC’s Europe Editor Katya Adler.
Quotas would be determined using a number of factors, including a country’s population, economic indicators and the number of asylum seekers previously accepted.
Germany keenly supports the idea of quotas, having received 200,000 asylum applications last year.
The proposed measures are the latest EU steps to stop migrants drowning in the Mediterranean.
On Monday its foreign policy chief, Federica Mogherini, will ask the UN Security Council to permit the use of force against people traffickers operating out of Libya.
Without a UN mandate, military action to destroy or halt traffickers’ boats in Libyan or international waters would be illegal.
Libya’s ambassador to the UN, Ibrahim Dabbashi, told the BBC that his country is against the proposal.
“The Libyan government has not been consulted by the European Union. They have left us in the dark about what their intentions are, what kind of military actions they are going to take in our territorial waters, so that is very worrying,” he told the Newsday programme.
Amnesty International has warned that military action could leave migrants trapped in Libya in desperate conditions.
“Introducing measures to tackle smugglers without providing safe alternative routes out for the people desperate to flee conflict in Libya, will not resolve the plight of migrants and refugees,” said Amnesty’s Middle East and North Africa director Philip Luther.
The new Amnesty report is titled “Libya is full of cruelty”. The title comes from a statement by an unnamed Nigerian migrant in the country.
Based on dozens of interviews of migrants the report documents stories of abduction, torture and rape.
It alleges that people smugglers are systematically abusing migrants. It also says that conditions in Libyan migrant detention centres are often appalling.
One Syrian family interviewed said that they were left with no choice but to attempt the perilous voyage.
“We were facing death in Libya so we thought we might as well face death in trying to get to Italy.”
The report calls on the international community to “dramatically expand search and rescue operations”.
European countries have already agreed to expand rescue services, having cut them last year.