Mr Barnier, who is rumoured to be considering running to replace French President Emmanuel Macron in the 2022 elections, demanded a halt to the European Union’s open-border policy.
He suggested a “three to five years” halt on non-EU immigration would help the union re-discuss the state of the Schengen Area and help tackle issues with the bloc’s migration system.
He claimed the “problems of immigration are not moderate” adding the bloc “must find solutions” and implement stricter “border checks”.
But the proposal was branded “racist” and “Trumpian” by the former Greek Finance Minister.
Mr Varoufakis blasted: “Michel Barnier is running for President.
“How do we know? He just played the hidden racism card, endorsing a Trumpian suspension of all migration into the EU.
“The inevitable slide of the extreme centre to xenophobic extremism.”
The Greek politician referred to former US President Donald Trump’s Executive Order 13769, also known as the “Muslim Ban” or travel ban.
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The temporary legislation lowered the number of refugees to be admitted into the United States in 2017 to 50,000, suspended the US Refugee Admissions Program (USRAP) for 120 days, suspended the entry of Syrian refugees indefinitely, directed some cabinet secretaries to suspend entry of those whose countries do not meet adjudication standards under US immigration law for 90 days, and included exceptions on a case-by-case basis.
The Department of Homeland Security (DHS) listed these countries as Iran, Iraq, Libya, Somalia, Sudan, Syria, and Yemen.
More than 700 travellers were detained, and up to 60,000 visas were “provisionally revoked”.
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Speaking on Monday, Mr Barnier said: “I haven’t changed my method.
“The problems of immigration are not moderate.”
He added: “I say as the political man that I am to look at the problems as there are, as the French live it, and to find solutions.
“I think we must take the time of three to five years to suspend immigration.”
But he clarified how he was not “talking about students, not talking about refugees.”
Mr Barnier stressed the importance of treating people seeking asylum and help on Europe’s shores “with humanity, with rigor.”
The Frenchman added: “But we must discuss with our neighbours the Schengen question, that we must apply border checks.
“That we have to be more rigorous.”