The forecasted shortfall comes as the EU plans to invest more into the protection of borders, tackling terrorism and defence.
EU leaders are set to discuss the budget gap at a summit on February 23.
Germany has stated it will make higher contributions to the EU after Brexit, the German news site Suddeustche Zeitung reports.
The figure is deliberately being kept open.
Germany’s willingness to pay more is not shared by Sweden, Denmark, Austria and the Netherlands, who are apparently resisting encouragement to join from Berlin.
It has been reported other countries will be reluctant to pay more when it will benefit countries the breach the EU’s rule, such as Poland.
The EU has launched disciplinary measures against the Eastern European country, arguing its judicial reforms threaten the rule of the law.
The bloc said 13 new laws in two years have allowed Poland’s government to “interfere significantly” in the judiciary.
The EU will also sue Poland, Hungary and the Czech Republic for refusing to take in asylum seekers.
Berlin and other EU capitals want to ensure countries such as Poland can only receive funds if they comply with the bloc’s laws.
EU Justice Commissioner Věra Jourová is proposing cash should only be distributed to countries that have a “functioning and independent judicial system”.
The EU Commission is divided as to whether that approach will work.
EU Commission President Jean-Claude Juncker and Commissioner for Structural Funds Corina Crete has called for a combination of EU aid and ensuring countries stick to the rules.
Mr Juncker has urged the remaining 27 EU member states tto pay more to fill the budget hole.
Speaking to an audience in Brussels in January after a BMG poll found that 51 percent of Britons support staying in the EU, he said: “There is going to be Brexit, of course.
“Don’t believe those who say that it’s not going to happen and that people have realised their error in the UK. I don’t think that is going to be the case.
“My working hypothesis is that the British are going to be leaving us on 30 March 2019. So between now and then, we need to do our utmost to fund the means to react to the loss of a significant number of billions of euros.”
The EU will be left with a funding gap of £11.5bn after the end of a likely transition period between March 2019 and December 2020.
The Commission claim that a half-and-half mix of new money and cuts be used to cover Britain’s withdrawal from the EU’s seven-year multi-annual financial framework.
Mr Junker said he wanted EU member states to agree by May to spend more than the existing 1% of GDP to maintain most of the bloc’s current programmes and meet future challenges, such as terrorism and climate change.