The party's apparent surprise backing for the EU and the euro will shock many, because it is aligned in the European Parliament with Ukip, which championed Brexit and is strongly anti-EU.
However, a letter sent by the party to the ALDE group seems to call into question 5 Star's stated policy aims.
The letter came amid attempts by Grillo, the 5 Star leader, to join the political mainstream by linking up with ALDE.
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That move came as a shock to many as 5 Star stands for a completely different set of ideals to those defended by European liberals.
Grillo founded the strongly Eurosceptic EFDD group in Parliament with Farage in 2014. 5 Star have in the recent past called for a referendum on Italy's membership of the euro.
One 5 Star source conceded that Grillo, a former clown who founded the party, has been criticised within the group of MEPs and there could be an attempt to replace him as leader.
The 5 Star letter, dated 4 January, states, "We believe only the European Union has sufficient weight to exploit globalisation, as a force for good and to ensure that the benefits are shared by all. The European Union must be the democratic counterweight to globalized economic forces."
It goes on to appear to give robust backing to the euro, saying, "During the past decade, our single currency has proven to be stable and resilient against external shocks."
It adds, "The European Union is first and foremost a community of values. We need to make European Union the global champion of civil liberties, fundamental rights and the rule of law."
The letter, headlined 'ALDE and Movimento 5 Stelle', says, !Shared values and mutual trust are key for EU policies such as police and justice cooperation, asylum and refugee policies, the digital agenda, energy or the joint management of external borders.!
On a possible alliance, the letter states, "ALDE and the 5 Star Movement share the core values of freedom, equality and transparency.
"We both see the individual as the central building block of society, while promoting an open economy, solidarity and social cohesion as the preconditions for people to achieve their full potential.
"We both want to strengthen the influence of citizens on decisions that affect them, including through developing mechanisms for direct democracy and by motivating people to participate and engage in politics."
One Parliament insider said, "This letter is quite incredible. 5 Star are in the same grouping as Ukip which has openly called for the EU to be scrapped. Yet in this letter to ALDE, Grillo was clearly defending the EU and the euro, one of its key cornerstones."
The letter was 5 Star's response to a possible alliance with ALDE, the group led by the arch-federalist Guy Verhofstadt's ahead of last week's vote to elect a new Parliament President.
Verhofstadt had been a candidate until he withdrew at the last minute.
The ALDE group later rejected the idea of any cooperation, formal or informal, with 5 Star and Verhofstadt was later criticised by some for considering the proposal.
An ALDE source told this website the link up was "totally unacceptable" to its members.
The ALDE move was thwarted by Liberals who were not ready to accept the anti-establishment group among their ranks.
After the botched - and highly improbable - link up with the Liberals, the maverick 5 Star remain part of the Eurosceptic EFDD group.
After the failure of Grillo's rapprochement with ALDE, one 5 Star MEP joined the Greens and another deputy defected to the extreme-right ENF group.