The row will dominate the summit, probably delaying a deal on dishing out the portfolios in the European Commission, say sources in Brussels. The powerful executive sets overall policy direction, administers the EU's 142.6 billion ($225 billion) budget, monitors member states for compliance to EU laws and is empowered to propose EU-wide legislation.
The outgoing incumbents of the top EU jobs are Van Rompuy and Catherine Ashton, High Representative for Foreign Affairs and Security. They were the first to be named to posts created with the idea of giving the EU a single voice on the world stage. Critics say Van Rompuy is best-suited to haggling in the backrooms of his home coalition politics in Belgium rather than being a strong leader for Europe.
Ashton swiftly became mocked after her appointment in 2009. A Labour Party loyalist close to former British Prime Minister Tony Blair, she was elevated to the role of top EU diplomat as a lowest-common-denominator compromise. Observers give her points for dogged negotiation with Iran on its nuclear programme but otherwise say she lacks the skills - but also the support from national leaders - to respond forcefully to fast-moving events.
The newly appointed head of the Commission, Jean-Claude Juncker, says it's time for a change. Ashton's successor "will have to be a strong and experienced player to combine national and European tools, and all the tools available in the Commission, in a more effective way than as we have seen it over the past months."
"The strategic environment has dramatically changed in the past few years, and the EU is probably weaker than it was five years ago in the eyes of many other countries in the world," notes Vivien Pertusot of the French Institute for International Relations in Brussels. "It may be high time to fix this situation, and a high-profile High Representative may help."
Italian Minister Federica Mogherini and Danish Prime Minister Helle Thorning-Schmidt
Others in the running for President include Danish Prime Minister Helle Thorning-Schmidt, a Social Democrat, but her country is not part of the eurozone. Italy has a good chance of pushing its Foreign Minister, Federica Mogherini, to replace Ashton although Poland and the three Baltic states - Estonia, Latvia and Lithuania - see her as too pro-Russian.
The eastern crisis is not the only factor in the wrangle, though. The left-wing and right-wing blocs of parties in the European Parliament also exert an influence, as do regional groups of countries, who feel that their voice should be heard louder. The candidate also has to strike a balance between big members and small ones. Jacob Funk Kirkegaard, an analyst at Peterson Institute for International Economics, warns a bustup this weekend would further dent Brussels' credibility. "If they can't agree on these posts, how will they manage Europe's deep economic problems?"
"The horse trading by the leaders of EU member states with regards to the selection of these two appointments is shameful. Their failure is due to fact that leaders dwell excessively on national interests," Franziska Keller, a member of the European Parliament with Germany's Greens Party, told the Herald in an email.