Writing in the New Statesman on Friday, Varoufakis said he warned Labour leader Jeremy Corbyn and shadow chancellor John McDonnell before the referendum that "after nearly four-and-a-half decades of entanglement with Europe, it would be very hard for the U.K.to leave even if it wanted to".
Concerns have also been raised about sweeping powers in the Withdrawal Bill that allow ministers to amend the law without going before parliament for as long as two years.
Theresa May has appealed for unity from pro-EU Conservative MPs as the Commons is set to debate the government's Brexit repeal bill on Thursday.
A Labour spokesman, who spoke on condition of anonymity, confirmed last week that Labour agreed to back "continued membership of the European Union single market beyond March 2019" in an attempt to offer a clear alternative to the Brexit now proposed by Theresa May's Conservative government.
Ahead of the debate, she said: Now it is time for Parliament to play its part.
Conservative divisions over Brexit will be laid bare this week when MPs scrutinise the complex legislation which will sever the UK's ties with the European Union.
He said: "The current draft of the Repeal Bill gives lots of power to ministers so we can deliver Brexit - which is essential - but it cuts Parliament's role right down". Green said that "no Conservative wants a bad Brexit deal", and a potential rebellion threatened to strengthen Labor's position.
But outspoken pro-Remain former minister Anna Soubry responded angrily to attempts to try to stop Tory MPs tabling or supporting amendments to the legislation, telling the Observer: "Any suggestion that this is in any way treacherous or supporting Jeremy Corbyn is outrageous".
Her allies have warned would-be rebels that they risk seeing Labour leader Jeremy Corbyn elected as prime minister if they attempt to water down the so-called Repeal Bill.
Brexit Secretary David Davis said a crunch point in the Brexit process comes in the week ahead, in Westminster rather than Brussels.
Meanwhile, Downing Street has denied a report that Theresa May is prepared to pay a £50bn divorce bill to the EU.
May was trying to expand her supporter base by winning over younger people who backed Labour in the June election with plans to reform tuition fees and provide cheap homes to public sector workers, the Sunday Times also said.
With the second reading of the bill on Thursday, and the vote the following Monday, the government has been pressuring potential Tory rebels to support the legislation which will transfer European Union law onto the UK's statute books.
"Were the United Kingdom government to propose such a transition, Michel Barnier, the EU's chief negotiator, would not be able to refuse", said Varoufakis.