Mr Reinfeldt (right) faces a difficult diplomatic balancing act as EU chair
Poland says contenders for the new top jobs of European Council president and EU foreign affairs chief should "present their visions" to EU leaders.
A Polish foreign ministry proposal, seen by BBC News, says the special EU summit on Thursday should "operate with transparency".
It says the appointments should result from a presentation, then discussion and a qualified majority vote.
Sweden, chairing the summit, has not called for any presentations.
As current holder of the EU presidency, Sweden says simply that "at the informal summit, which will take the form of a working dinner, it is hoped that an agreement can be reached" on the appointments.
Sweden's Prime Minister Fredrik Reinfeldt has had intensive consultations with EU leaders ahead of the summit to try to get agreement on two candidates for the top two jobs. That would make any vote a formality.
Runners and riders
Belgium's Prime Minister Herman van Rompuy is reported to be the frontrunner for the job of European Council president, but his rivals include Dutch Prime Minister Jan-Peter Balkenende, former Latvian President Vaira Vike-Freiberga and the UK's former Prime Minister Tony Blair.
THE PRESIDENT'S ROLE
Chosen by 27 member states by qualified majority vote
Drives forward the work of EU Council of Ministers
Facilitates cohesion and consensus
Represents the EU on the world stage
Italy's former Prime Minister Massimo D'Alema and Swedish Foreign Minister Carl Bildt are reported to be top contenders for foreign affairs chief, who will be called the High Representative.
The EU leaders are expected to strive for a balance in these two key posts, with one likely to be filled by a big country candidate, the other a small country. Similarly, the presidency job is expected to go to a centre-right politician and the foreign affairs job to the centre-left.
A third post - Secretary-General of the European Council Secretariat - will also be decided. That person will be a top civil servant, managing the council's business.
Poland has reminded its EU partners that, under the Lisbon Treaty, the appointments of president and foreign policy chief ought to be made by qualified majority vote.
Before the vote, Poland suggests, the candidates should "present their visions... of how their tasks would be conducted".
"We do believe that our position on the selection procedure has been met with a positive response of a significant number of member states," Polish foreign ministry spokesman Piotr Paszkowski said.
Mrs Vike-Freiberga has echoed Poland's concern that the selection process should be "transparent" and has also urged the EU to consider appointing a woman.
The BBC's Europe editor Gavin Hewitt says confusion surrounds the summit proceedings.
It is not clear how the dinner will be conducted, nor whether there will be a wide-ranging discussion of various candidates, he says.