According to the Financial Times, several EU officials, including Luxembourg's foreign minister Jean Asselborn, warned Greece that unless it improved the conditions for refugees entering the country and boosted border controls, then it could face suspension from the 26-state free movement zone.
Slovak Prime Minister Robert Fico seemingly backed the veiled threats of Greece's suspension from the Schengen.
"We just cannot put up with a member country that has openly given up on safeguarding the Schengen area borders. Then Schengen is of no use."
During a meeting in Brussels this week, EU ministers are expected to ask Greece to step up efforts to control the flow of migrants and refugees into Europe, improve the registration of refugees and boost cooperation with the EU on the issue.
More than 740,000 people have arrived on Greek shores this year, including many on Greek islands in the Mediterranean.
However the country, battling its own economic crisis, has struggled to provide adequate services to many refugees arriving on Greek shores, with serious humanitarian concerns over the conditions greeting migrants.
Greece Hits Back
Despite criticism from EU officials and other member states, Greek officials have defended the country's actions in the trying circumstances, noting that there had been private threats made over possible suspension from the Schengen zone.
"It is not said officially, but there is pressure," Greek Migration Minister Yiannis Mouzalas said.
"These are very common lies for Greece… This blame game towards our country is unfair."
Mouzalas defended Greece's handling of the refugee crisis, saying the country had spent an extra US$1 billion in additional unbudgeted funds to help with the refugee crisis, despite the country's strained economic state.
He added that so far only US$30 million worth of EU assistance had reached Athens due to bureaucracy on both sides.
Strange EU officials make threats re: Greece & Schengen right after satisfying Turkey demands due to source of migration problem lying there— Nick Malkoutzis (@NickMalkoutzis) December 1, 2015
Despite threats to suspend or expel Greece from the Schengen zone, Estonian Prime Minister Taavi Roivas warned against such action, telling Reuters that suspending Greece from the free movement zone would not be helpful.
"The problem is definitely there and I do know that we need to work together to solve it. But building fences between us is not a long-term solution."