The vote has been made possible after officials in the Council of Ministers were able to speed up work on the EU's data protection legislation.
The proposed EU PNR directive would oblige airlines to hand EU countries their passengers' data in order to help the authorities to fight terrorism and serious crime.
Under the Commission proposal, air carriers operating flights between a third country and the territory of at least one EU member state would be obliged to send PNR data to the competent authorities of that member state.
Carriers would send this data by the so-called "push" method, meaning that member states would not have direct access to the carriers' IT systems.
Member states would share "alerts" created from the processing of PNR data for the prevention, detection, investigation and prosecution of terrorist offences or serious crime, for example, human trafficking, drug trafficking, or child pornography.
Member states would also have the right to request PNR data from another member state in support of a specific investigation.
The collection and use of sensitive data directly or indirectly revealing a person's race or ethnic origin, religious or philosophical belief, political opinion, trade union membership, health or sexual life, would be prohibited.
The Commission proposal would allow PNR data to be retained for five years and 30 days.
The provisional deal reached by Parliament and Council negotiators last December was endorsed by the civil liberties, justice and home affairs committee.
MEPs had sought to ensure, in three-way talks ("trilogues") with the Council and Commission, that the draft law complies with the so-called proportionality principle and includes strict personal data protection safeguards.
Hundreds of amendments have been tabled to the original proposals by MEPs from various political groups, but a vote on data protection is now finally scheduled in the home affairs committee on Monday, with both data protection and PNR voted in the plenary on Thursday.
The aim the data directive is to put internet users in control of their personal data and to regulate data transfers to third countries, while a regulation sets new standards on use of data for policing and judicial purposes.
The PNR proposal has dragged on for many months and has been criticised by some, including the Greens, who brand it an infringement to civil liberties.
"All the perpetrators of the Paris attacks were already known to the security services, "said French Green MEP Pascal Durand. "What is really lacking in Europe is not the access to information, but the personnel to deal with this information," he added.
"If we could prove that a European PNR would have been useful to obtain information that could have stopped the Paris attacks, then obviously we could reopen discussions on the text. But for now, we are just meddling with a disproportionate surveillance system," the MEP said.
But Parliament's lead MEP on PNR, British Tory Timothy Kirkhope, welcomed the news that Parliament is set to vote on the proposals.
Kirkhope, who has been working on the PNR proposals for nearly five years, said: "Finally it looks like we are going to vote on EU PNR. It's been five years in the making with many setbacks and much negotiation, but I believe the EU and the UK need this tool urgently.
"PNR will provide us with a vital way of detecting foreign fighters, drug traffickers and serious criminals.
The deputy went on, " Rather than 28 different national systems being created we are now set to have a single law enabling the collection and sharing of information to give intelligence agencies a full picture, and to ensure robust privacy protections across the whole EU."