PRAGUE - Four ex-communist eastern European Union members will propose outgoing European Commission Vice President Maros Sefcovic as their candidate to head the new European Union executive, Czech newspaper Hospodarske Noviny reported on Tuesday.

Citing Czech and EU sources, the paper said the Czech Republic, Slovakia, Hungary and Poland -- known as the Visegrad Four -- could also push Sefcovic, a career diplomat, to take the EU's foreign policy post if he cannot secure the top spot.

Leaders of EU member states will meet on Tuesday evening to assess the outcome of last weekend's European Parliament election and begin the process of bargaining over EU leadership jobs and policies.

Moscow-educated Sefcovic, 52, has been a Commission member since 2009 and currently oversees EU energy policy.

He was backed by Smer, the leftist party that has dominated Slovak politics since 2006, in Slovakia's presidential election in March, but lost to liberal lawyer Zuzana Caputova, who surged to victory on a wave of public fury over corruption.

In that election he said he wanted to fight back against a rising tide of euroscepticism sweeping the European Union.

Sefcovic had said last year that he would stand for the Commission presidency but later withdrew his bid and endorsed the EU's deputy chief executive, Dutchman Frans Timmermans, a fellow member of the Party of European Socialists.

In Brussels, Sefcovic was not immediately seen as having a strong chance.

Horse-trading over the EU's top jobs, taking into account national interests, party lines and gender issues, will last at least until a June 20-21 summit.

A standoff is shaping up with parliament, where most EU party chiefs want the national leaders to endorse the assembly's pick to replace Commission President Jean-Claude Juncker.

Other names in the running to include Timmermans, already nominated as the Socialists' lead candidate for the top Brussels job, the EU's Brexit negotiator, Frenchman Michel Barnier.

(Reporting by Robert Muller; Additional reporting by Gabriela Baczynska in Brussels; Editing by Catherine Evans) ((robert.muller@thomsonreuters.com; +420224190475; Reuters Messaging: robert.muller.thomsonreuters.com@reuters.net))