Several deputies hope to succeed Martin Schulz in Parliament's top job. The German MEP's decision to return to German domestic politics triggered the election.
Guy Verhofstadt, ALDE group leader, Gianni Pittella, who heads the S&D group and Antonio Tajani, of the EPP group, are among those who have agreed to take part in the Q&A session with the Greens group.
Two other candidates will also take part - Eleonara Forenza, a GUE/NGL member and Helga Stevens, of the ECR group.
However, a sixth candidate, UK Greens MEP Jean Lambert, will not be questioned by her own group.
Three Italian deputies are in the running for the post, which will be decided in a secret ballot.
On Monday, a source with the Greens group explained why they had decided to organise this week's meetings.
He said, "It is in order to gain a better understanding of the candidates of the other political groups for the presidency. We invited them to give a short presentation and take questions from our group."
The sessions in Parliament on Tuesday and Wednesday are public and all are invited to attend, he said.
The coming contest on 17 January is more open than most previous presidential elections, because whereas in the past the mainstream parties have struck a deal in order to appoint a presidential candidate, the EPP and S&D groups will this time compete directly against each other.
Tajani, a former spokesperson for Silvio Berlusconi, is a clear favourite but, even so, will still need to win backing from a wide range of MEPs, including the ECR and ALDE groups and even more populist parties if he is to win.
The EPP group currently holds 216 of 751 EU Parliament's seats, while the Socialists hold 189 and the Liberal alliance holds just 68.
Tajani previously served as a European Commissioner after being appointed by Berlusconi.
In declaring his candidacy, Pittella has severed a long-standing power-sharing agreement that called for the presidency to pass from the S&D, the second-largest group in Parliament, to the EPP in January 2017.
Verhofstadt, who is also Parliament's main Brexit negotiator, said he offers the only chance to stop the centre-right EPP "taking control of the chamber."
On her hopes, Forenza told this website, "I am a feminist from the south of Europe. This in itself makes a strong political statement and I am acutely aware of the heavy responsibilities this carries," she continued.
"I will work to make the Parliament the centre of a project for a Europe built on the full participation of its citizens in politics.
"Having a fully democratic Europe means radically changing the current set-up in the European Union: a model that is based on neoliberalism, on austerity, on budget constraint, on the sovereign debts and the blackmails.
"In addition, the lack of recognition of the right to work and the minimum income - particularly in southern Europe - must be reversed. Similarly, an oversight of fundamental rights for women and migrants are all elements which must be changed inside the EU where a third of women have suffered physical or psychological abuse," she continued.
During next week's Strasbourg plenary, Parliament will also fill all other leadership positions, including vice-presidents and committee chairs. The positions are filled using the D'Hondt system, a mathematical formula which aims to distribute seats in the most proportional way.