The decision by the bloc's 28 leaders came on Friday during a two-day meeting in Brussels.
The report says the leaders agreed to use "all possible levers, including... reassessing visa policy towards third countries".
"We can use visas to convince them to take returns," said a senior EU diplomat, adding the move would, among other things, target the ruling elites of these countries as they can afford trips to Europe.
Immigration has been a prime concern for the bloc amid the spike in arrivals across the Mediterranean since 2014.
Some countries, including Bangladesh and Nigeria, are often reluctant to readmit their citizens and the EU has recently doubled down on efforts to expedite such returns, according to the Reuters report.
Italy is now the key entrance point to the bloc and most of those reaching European shores after boarding smugglers' boats in Africa are considered illegal labour migrants.
EU states remain at loggerheads over how to handle refugees who make it into the bloc, yet they have decided to gloss over the issue after two years of divisive feuds.
The assurance was made in May during a meeting in Brussels between Law Minister Annisul Huq and European Commissioner for Migration, Home Affairs and Citizenship Dimitris Avramopoulos.
Bangladeshis now make up the single largest group of illegal migrants to European shores, according to a recent report by London-based newspaper The Independent.
More than 2,800 Bangladeshis arrived on European shores from North Africa in the first three months of 2017, compared to only one over the same period in 2016, says the report published in May.
With a record of almost 1,100 people drowning, suffocating or dying of hypothermia on overcrowded boats so far this year, the North Africa to Italy crossing is considered the deadliest sea passage in the world.
EU leaders called for further action to stem the flow of migrants from Libya to Italy, along the Central Mediterranean route, the European Council said in a statement. They also reiterated the need to reform the common asylum system.