Mr Juncker was elected through the Top Candidate System back in 2014, which sees parties nominate top candidates and the candidate of the party that gets the most votes becomes Commission President.
The EU Parliament thinks this is the most ‘democratic’ way to decide.
However, a significant number of EU leaders have reservations. Especially French President Emmanuel Macron, whose “En Marche” movement belongs to no European party family.
So who is in the running to take over Mr Juncker’s job?
Michel Barnier
EU Brexit negotiator Mr Barnier is considered highly competent, modest and loyal.
He put himself forward for President in 2014, but lost the top spot to Mr Juncker.
If Mr Barnier manages to negotiate a Brexit deal acceptable to Brussels and London, the European Conservative vote will be almost guaranteed.
However, some Europeans think he is exaggerating his hard line with London.
Margrethe Vestager
The 49-year-old Dane is serving as European Commissioner for Competition.
She is very popular and ambitious.
Ms Vestager is socially liberal and thus potential alliance partner of Macron.
Despite her popularity, her party is no longer in government and the Danish Prime Minister has hinted he does not want her to stay another term in Brussels.
Federica Mogherini
Ms Mogherini received a lot of criticism when in 2014 she was appointed EU Foreign Affairs Commissioner after only a few months as Italian Foreign Minister.
Critics said she was too young, too inexperienced and too Russia-friendly.
Four years later, the Social Democrat has worked hard to establish a solid reputation and is not afraid to go head to head with Vladimir Putin or Recep Tayyip Erdogan.
However, many think it unlikely the top role would go to a leftist.
Mr X
The question of who will eventually become President of the European Commission always depends on the distribution of other EU top offices such as the permanent President of the Council, the President of the European Parliament or the Chairman of the European Central Bank.
Sometimes the top candidate can come from nowhere.
One insider tip is Lithuanian president Dalia Grybauskaite. She has a good reputation among EU heads of state and government and is experienced in Brussels business from her time as EU Budget Commissioner.
Her Baltic background could act as a possible bridge-builder between East and West.
(Additional reporting by Monika Pallenberg.)