The agreement was reached during a teleconference of the Eurogroup Working Group (EWG), which started at 1300 GMT on Monday and lasted for about one hour.
As well as confirmation from two officials, Reuters has seen a memo drawn up by one member state detailing some of the elements that euro zone countries should consider.
The EWG consists of officials who prepare meetings of finance ministers and also form the board of the temporary bailout fund, the European Financial Stability Facility (EFSF).
"The EWG agreed that each euro zone country should prepare a contingency plan, individually, for the potential consequences of a Greek exit from the euro," said one euro zone official familiar with what was discussion on the call. "Nothing was prepared so far on the euro zone level for now, for fear of leaks," the official said.
A second official confirmed the EWG agreement on Monday.
The document detailed the potential costs to individual member states of a Greek exit and said that if it came about, an "amiable divorce" should be sought. It also said that Greece decides to leave, support could be given from the EU/IMF to help it do so.