Among the abuses cited are unlawful residency and unfounded asylum claims.
The document, dated September 27, comes as European Commission President Ursula von der Leyen tours the Western Balkans.
The EU visa regime for Montenegro, Serbia, and North Macedonia was abolished in December 2009, followed by Albania and Bosnia in 2010, Moldova in 2014, and Georgia and Ukraine in 2017.
Visa-free travel for up to 90 days to the EU has been considered an important step ahead in the 27-member bloc's relations with the Western Balkans and the former Soviet states under its Eastern Partnership policy.
But according to the document, Germany, France, and Italy have recently become more and more frustrated with alleged abuses of visa-free travel. It mentions surges in "unauthorized residence offenses" perpetrated by citizens of Albania, Moldova, Ukraine, and Serbia.
The document also listed a more than 50 percent increase in Georgian asylum claims over the past three months, compared to the same period in the pre-coronavirus pandemic year of 2019.
Under the so-called Visa Suspension Mechanism, a rise of more than 50 percent in illegal stays or asylum applications with low approval rates can lead to visas being reintroduced.
Furthermore, refusal by governments to readmit their nationals can also see the return of visas.
In the document, Germany mentioned Moldova as a particularly serious case, with a 429 percent surge between June to August 2019 and June to August of this year.