She has been chosen as the GUE/NGL group candidate for the presidency, which is now up for grabs after the current incumbent, Socialist deputy Martin Schulz, decided to return to German politics.
Forenza joins a growing list of MEPs who have declared their candidacies, including Italian Gianni Pittella, S&D group leader, and Belgian deputy Helga Stevens, from the ECR group.
She has little chance of success but has called for an end to the so called "grand coalition" that has repeatedly seen the presidency shared between the EPP and Socialists, the two biggest political groupings in the institution.
Other possible candidates include EPP group Chair Manfred Weber, while ALDE's Guy Verhofstadt has also been touted.
Support for an end to the grand coalition also comes from an unlikely quarter, as Pittella's group strongly opposes the EPP taking the post being vacated by Schulz. An EPP President would mean each of the EU's three presidencies, Commission, Parliament and Council, are held by politicians from the EPP family.
A secret ballot vote on who will be the new President will be taken by MEPs in Strasbourg in January.
Speaking after the decision to stand, Forenza said, "I want to thank GUE/NGL for the trust they have placed in me by putting forward my candidature for Parliament's presidency.
"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.
"Last Sunday, the Italian people defended the country's anti-fascist constitution which dates from the time of the resistance by voting 'no' to a constitutional reform aimed at reducing the powers of the Parliament - something which JP Morgan had clearly wanted for countries in southern Europe. But democracy prevailed and the European governance that wants to impose structural reforms to member states has lost."
"Meanwhile, in the European Parliament, the so-called grand coalition between the S&D and EPP wants to pass through the undemocratic review of the rules of procedures. This is the same grand coalition that has supported austerity.
"We will fight against any attempt to restrict the rights of minority groups and of every elected representative in this Parliament. This is happening right now with the imminent approval of the Corbett report on the new rules of procedures in Strasbourg next week.
"Europe needs more democracy - not less. I hope my candidacy will find support among those who wants to build another Europe - a fully democratic Europe. An alternative Europe to the one envisaged by the grand coalition," the Italian MEP added.
Commenting on Forenza's candidature, GUE/NGL group leader Gabi Zimmer said, "As the Left group in the European Parliament, we will continue to offer a political alternative to the people in the EU: against unacceptable austerity; building a genuine social pillar for the EU; investing in a sustainable and inclusive development and on decent work; for tax justice and a fairer distribution of wealth; for the respect of human rights and against the inhumane Fortress Europe.
"We will fight for a more democratic EU based on solidarity where policies are made for a majority of people - not just for banks and transnational corporations," Zimmer said.