The idea is contained in the policy document drafted by Parliament's EPP and ALDE groups.
The two political groups joined forces to sign an agreement shortly before the recent contest for Parliament's presidency.
Under the deal, the two groups have agreed to form what they call a "pro-European coalition".
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One of the key recommendations of the document, which has been seen by this website, is a proposal for an inter-institutional convention, similar to the one set up several years ago to debate the possibility of a formal written constitution for Europe. The idea was later rejected and some branded the convention as a "waste of time and money."
The new EPP-ALDE agreement suggests that Parliament proposes to the EU's two other institutions - Commission and Council - "the launch of a common, inter-institutional reflection on the future of the European Union."
It adds, "This reflection must include the possibility of launching a convention. We need leadership, the future does not wait."
The EPP and ALDE groups joined forces after an attempt by the Italian 5 Star Movement to link up with the Liberals was rejected by ALDE group Chair Guy Verhofstadt.
The EPP, Parliament's biggest group, and ALDE, subsequently launched what they call a "common platform" for the second half of the current legislature.
In return, Verhofstadt dropped out of the race to become Parliament's next President and ALDE agreed to back Italian MEP Antonio Tajani, the EPP candidate and eventual victor.
The agreement has been strongly condemned by the Socialist group, who themselves previously had entered into a deal with the EPP, known as the grand coalition, which traditionally saw the presidency shared between the two biggest groups.
However, the EPP and ALDE groups defend their newly-forged alliance, because they say "Europe is in crisis."
The two-page document reads, "Nationalists and populists of all boards try to destroy the Union from within and from outside. A pro-European coalition is needed to withstand this attempt.
"A cooperation of all the pro-European groups and MEPs in the House not to defend the status quo, but to deliver on the needs of the European citizen and to reform the European Union.
"Therefore, the EPP and ALDE - beyond their ideological differences - have decided to work closely together and to offer a common platform as a starting point for this pro-European cooperation."
It goes on, "We appeal to all other pro-European forces in the House to join this initiative and to add their ideas and their priorities to our agenda of reform."
On the policy front, the two groups signal out two areas where they say they can cooperate.
The draft says the focus should be on "environmental policies and in particular the implementation of the Paris agreement and the further development of the European emission trading system."
Other issues such as further deepening of the internal market especially in the field of digitalisation and energy, fight against bureaucracy, fair taxation and social cohesion "will have high priority."
Both groups will, according to the paper, "act to ensure the full involvement of the European Parliament in the Brexit negotiations so that the interests of the European citizens are fully taken on board."
It says, "The European Parliament resolution will clearly indicate that the presence of the Parliament (besides the Council) in the EU negotiations is a pre-condition for the consent procedure."