EBA staff with children will be given flexibility to stay in London beyond the March 2019 cut-off point, when the UK leaves the EU.
No formal request to the European Commission to extend the EBA's London tenure has yet been made, City A.M. understands.
However, EBA chair Andrea Enria said the extension could be "four or five months" to allow children of employees to finish the school year, in an interview with Financial News.
The agency, which has around 180 staff, has previously coordinated regulations covering both Eurozone and non-Eurozone nations, although after Brexit it will lose its most important non-euro banking system.
The staff have been forced to leave London after the Brexit vote, with the French capital winning a competitive and arcane bidding process. It beat off other European banking centres, including German financial capital Frankfurt, and finally emerging victorious over Dublin after a tie when its name was pulled out of a hat.
The EBA is currently headquartered on the 45th floor of One Canada Square in Canary Wharf, a building it shares with banks including BBVA and the Bank of New York Mellon.