Their priorities include compiling a list of countries whose nationals would not be considered asylum seekers, aside from exceptional personal circumstances. The European Union has previously failed to draw up a common list of such countries.
The French and German leaders will also try to speed up the establishment of reception centres in overwhelmed Greece and Italy to help identify asylum seekers and illegal migrants.
In June, European Union governments rejected a push by Commission President Jean-Claude Juncker to set mandatory national quotas for states to take in some of the tens of thousands of refugees and migrants crowding ashore in Italy and Greece.
Italian officials said this weekend that the coastguard had rescued 4,400 migrants from 22 boats in the Mediterranean on Saturday alone in what was understood to be the highest daily figure in years.
Meanwhile, at least 2,000 more migrants entered Serbia overnight from Macedonia, which had declared a state of emergency over the massive numbers pressing into the country from the Greek border.
EU border agency Frontex said last week that a record 107,000 migrants were at the bloc's borders last month, with 20,800 arriving in Greece last week alone.
"There has to be a new impetus so that what has been decided is implemented," a source in the French presidency told news agency AFP, referring to EU decisions taken in June to tackle the crisis.
"The situation is not resolving itself," the source said, adding that the decisions made by the EU "are not sufficient, not quick enough and not up to the task".
Meanwhile, Merkel on Monday condemned anti-immigration riots in eastern Germany as “repulsive,” her spokesman told media, after police guarding a refugee shelter were attacked by protesters for three consecutive nights.
The German government said last week that it expects 800,000 refugees to arrive in Germany this year. Over the first six months, 220,000 people have already arrived, fleeing war, violence and poverty in Asia, Africa and the Middle East.
Germany alone hosts 40 per cent of refugees hosted on European soil, German Foreign Minister Thomas de Maizière said.
Beyond the migrant crisis, Merkel and Hollande will also meet with Ukrainian President Petro Poroshenko to discuss the recent resurgence of violence in Ukraine.
The talks will be notable for their diplomatically-charged exclusion of Russian leader Vladimir Putin.
Poroshenko on Monday accused Russia of sending major military backup to pro-Moscow rebels in eastern Ukraine.