Germany and Italy's interior ministers have written to the European Commission calling for an EU-wide system to register migrants, according to reports in a German newspaper.
The two country have also called for a harmonisation of selection procedures and rights for asylum seekers.
In the letter seen by Sueddeutsche Zeitung, German Interior Minister Thomas de Maiziere and Italy's Angelino Alfano called for an "ambitious reform" of the Dublin rules - which oblige migrants to request asylum in the first EU country they enter - by means of a "newly adjusted Common European Asylum System".
The EU has been seeking to establish a Common European Asylum System since 1999 but differences between member countries have persisted despite attempts to unify asylum laws in the bloc.
In their letter to European Commission First Vice President Frans Timmermans and EU Migration Commissioner Dimitris Avramopoulos, the two ministers said an EU-wide registration mechanism that includes security checks should be set up with the help of EU border agency Frontex.
They also called for a harmonisation of the differing conditions throughout the bloc for accepting migrants, selection procedures and rights for asylum seekers.
They said the EU's Asylum Support Office should get extra staff and funds so it could become a "real European asylum agency".
They suggested identifying people in need of protection within their countries of origin or transit countries before bringing them to Europe - the approach currently being pursued in the EU's cooperation with Turkey - and said the aim was to create an "institutionalised relocation system in the EU".