Such a budget, outside the seven-year framework of the 27-member EU, could centralise tax and spending decisions.
The draft EU summit conclusions say "mechanisms for fiscal solidarity, eg via an appropriate fiscal capacity, should be explored".
UK Prime Minister David Cameron says the eurozone will need its own budget
The draft conclusions say the eurozone's own "fiscal capacity" - that is, a budget - would be "specific to the euro area and therefore not be covered by
the Multiannual Financial Framework". That framework is the EU's long-term budget, amounting to about 1% of the EU's GDP.
The EU is beginning negotiations on its next budget for 2014 to 2020. Mr Cameron has warned that he will block any "massive increases" in that budget.
The idea of launching a separate eurozone budget was floated by European Council President Herman Van Rompuy in an issues paper in June.
Last December Mr Cameron vetoed an EU-wide treaty to co-ordinate budget policies and impose penalties on rule-breakers. The fiscal compact, in line with German demands for budgetary rigour, is binding on signatory states but is not an EU-wide treaty because of the UK veto.
In a BBC interview on Sunday Mr Cameron said "there will come a time I believe where you're going to need to have two European budgets - one for the single currency, because they're going to have to support each other much more, and perhaps a wider budget for everybody else."
The EU leaders also plan to discuss "contractual" agreements between eurozone states and EU institutions, to make economic reforms binding.
"The idea for the euro area Member States to enter into individual arrangements of a contractual nature at the European level on the reforms they commit to undertake and on their implementation should be explored," the draft summit conclusions say.
Such contracts could be modelled on the binding austerity measures now in place in Greece, Portugal and the Republic of Ireland - the recipients of massive EU bailouts. The measures are aimed at preventing the accumulation of excessive debt and are a condition for the bailout instalments.