The European Investment Bank will consider a capital increase to allow EU nations to increase their stake after Britain pulls out of bank in March.
Britain – the biggest EIB shareholder – leaving the EU would mean the bank losing €3.5bn (£3.1bn) of capital.
Other existing shareholders will increase their stake proportionally to make up for the loss, an EU official told Reuters.
The EIB, owned by European Union governments, will need to replace the UK capital to secure its AAA credit rating.
The bank is working on a separate plan to allow some countries to raise their holding.
The official said: “Poland has been vocal that it wants to increase its stake in the EIB, because the size of its economy has grown substantially since it entered the European Union in 2004.”
A country's stake in the EIB is based on its relative economic weight within the bloc based on its GDP on joining the EU.
Most EU members want a capital increase proportional to the current shareholders' composition but Polish Prime Minister Mateusz Morawiecki said Warsaw was willing to be “very tough” in its pursuit of a greater holding.
Poland's GDP has grown to $614bn from around $217bn when it entered the EU.
Sweden, Denmark, Belgium and Austria all have bigger stakes in the EIB and a lower GDP.
EU officials also said Spain was interested in raising its holding, although it was no clear how much capital on top of the amount needed by the Brexit rejig it was willing to contribute.
The EIB will present its findings on a potential capital increase at a meeting in Bucharest on 17 September.
The bank now has 243.3 billion euros of capital, of which 21.7 billion is paid in.