Poland has said it may drop its opposition over voting rights to allow a deal on a new EU constitution.
Both leaders want the new EU constitution adopted in 2004
"We believe that a compromise is not only necessary but possible," Polish Prime Minister Leszek Miller said.
He was speaking after talks in Warsaw with German Chancellor Gerhard Schroeder, who said Berlin would stick to a voting system in a draft text.
Last year, the EU failed to agree on the draft text because of opposition from Poland and Spain.
Both countries have been keen to preserve voting rights in the Council of Ministers in an expanded EU, under a 2000 agreement that gives them a greater say than their population would warrant, compared to Germany, France, Britain and Italy.
But Spain's incoming Prime Minister Jose Luis Rodriguez Zapatero has already promised to look again at the policy.
Given that the German and French leaders last week signalled they would not be moving on their positions - that would mean Poland backing down, the BBC's Ray Furlong in Berlin says.
On Tuesday, Mr Schroeder stressed that the new voting system should be based on the "double majority" principle proposed in the draft constitution.
Under the proposal, EU laws would be adopted by a majority of member states representing 60% of the population.
But Mr Schroeder added that any future agreement must also reflect Poland's demands to have a bigger say in the EU.
Both Mr Miller and Mr Schroeder expressed hopes that the constitution would be adopted "under the Irish presidency" - which end on 30 June.
The EU constitution is aimed at improving the efficiency of the bloc after it grows to 25 members from the current 15 on 1 May.
Poland is by far the largest country set to join the EU.