A meeting in Brussels on Thursday and Friday of EU heads of government is expected to elect the new Council for the period from 1 June 2017 to 30 November 2019.
Donald Tusk's 30-month term as the President of the European Council is due to end on 31 May.
Malta, which currently holds the Council's rotating six-month presidency, will oversee the process of choosing the Council chair.
Polish centre-right MEP Jacek Saryusz-Wolski, who is a member of the Civic Platform (PO) party in Poland, took the unusual step of accepting the nomination of Poland's ruling Law and Justice party to run against Tusk.
Tusk is Saryusz-Wolski's compatriot and fellow member of the Civic Platform. Tusk - a former Prime Minister of Poland, is co-founder of PO.
On Saturday, the Polish foreign ministry officially announced that Saryusz-Wolski, an EPP group deputy and former Chair of the foreign affairs committee, would be forwarded as Warsaw's official candidate for the post.
The governing PiS party, which has fallen foul of the Commission in recent weeks, also confirmed that Poland will not support Tusk's bid for a second term.
Saryusz-Wolski's acceptance of the nomination has caused some friction in the EPP group and on Monday there was widespread speculation that he would be excluded from the group.
Former French deputy Joseph Daul, President of the pan-European European People's Party, reportedly said, "I deeply regret Saryusz-Wolski's disloyalty and disrespect towards the unity and values of his own member parties, Civil Platform (PO) and the EPP."
An EPP source said that its position on the Council presidency remained "clear and unchanged."
The source said, "Donald Tusk has the EPP's unequivocal support to continue for a second mandate in his current position."
In a series of tweets, Manfred Weber, the leader of the EPP group in Parliament, made his views clear, saying, "Tusk is the only EPP candidate for President of European Council. He enjoys unanimous support from the entire party family."
The EPP is the largest and most influential European-level political party of the centre-right, which currently includes 79 member parties and partners from 41 countries.
It currently holds the presidencies of the European Commission (Jean-Claude Juncker), the European Council (Tusk) and the European Parliament (Antonio Tajani).
It also has seven EU and five non-EU heads of state and government, 13 members of the European Commission and the largest group in the European Parliament.