The top IMF experts believe that a possible Greek default on its third bailout would coincide with Britain's possible Brexit and it would be hard for the EU to deal with two major events at the same time.
"This is going to be a disaster," Velkouleskou said during the meeting.
According to the leaked conversation, the IMF wants to tell Germany that it will leave the Troika, composed of the IMF, European Commission and the European Central Bank, if the IMF and the Commission cannot reach an agreement regarding the Greek bailout.
The IMF chiefs want Greece to accept more austerity measures, such as raising taxes and cutting pensions. According to the leaked conversation, Greece needs to accept more of these draconian measures or the EU will face the threat of "an imminent financial catastrophe."
However, the Brexit referendum in June "will paralyze European decision making at the critical moment," the IMF officials fear, according to WikiLeaks.
Last August, the Troika approved an 86-billion-euro bailout package aimed at re-building Greece's economy in exchange for reforms and austerity measures.
Meanwhile Britain will vote on whether or not the country should remain in the EU. Supporters of Britain exiting the union argue that EU membership has eroded the nation's independence to make laws, direct its economy and control its national borders. Opponents say that leaving the EU could seriously harm Britain's economy.