Over a dozen member states have already thrown their hats into the ring to host the European Medicines Agency (EMA) and the European Banking Authority (EBA), currently housed in London's Canary Wharf business district.
EU President Donald Tusk and European Commission head Jean-Claude Juncker will bring up the sensitive topic at the summit in Brussels where the 27 remaining EU leaders will adopt Brexit negotiating guidelines, European officials said.
EU leaders will then vote on a list of contenders later in the year, with Tusk intending to name the new hosts at a summit in either October or December, another senior EU diplomat said.
At least initially, the EU will push Britain to pay all relocation costs, the diplomat said, amid reports that owed rent in London could reach hundreds of millions of euros.
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It is a major acceleration of the process of moving the agencies ahead of Britain's exit from the EU in March 2019.
Luxembourg in March fired an opening shot, claiming that it had a legal right to win the EBA based on a statute from the 1960s that gives the small duchy first dibs on any EU agency involving the economy.
The EBA is perhaps best known for its regular stress tests on the EU's financial sector, which have become a vital focus for investors and regulators in the wake of the global financial crisis.
Spanish Prime Minister Mariano Rajoy yesterday wrote EU officials to defend Barcelona as a host of the EMA.