Greece has admitted it joined the euro in 2001 on the basis of figures that showed its budget deficit to be much lower than it really was.
Greece's finance minister has vowed to tackle the deficit
Eurozone states are expected to have deficits below 3% of gross domestic product but revised data show Greece has exceeded that limit since 1999.
The figures are being discussed at a meeting between EU finance ministers.
Greece's membership of the single currency would not, however, be questioned, the EU has said.
Greek press reports suggest the country's budget deficit in 1999 was 3.38%.
Eurostat, the EU's statistics agency, visited Athens last week to examine Greece's budget figures.
Greece had already said that its public deficit breached the European Union cap between 2000 and 2003, as the cost of hosting the 2004 summer Olympics reached 7bn euros (£4.8bn).
But Greece's finance ministry had claimed that the country's 1999 deficit, on the basis of which Greece was allowed to join the euro in 2001, was below the limit.
"It has been proven that Greece's budget deficit never fell below 3% since 1999," finance minister George Alogoskoufis admitted on Monday.
Katinka Barysch, chief economist at the Centre for European Reform, said the announcement would not be a surprise for Brussels insiders.
"Quite a few member states did something similar because of the political imperative to join the euro as soon as possible. Greece has just gone a bit further," she said.
France and Germany have previously defied the 3% limit.
With the European Central Bank (ECB) currently telling East European member states that want to join the euro that they must strictly adhere to the 3% rule, the EU risks being accused of double standards, Ms Barysch said.
"These countries will say the ECB wants them to be holier than the Pope," she added.
A decision on possible disciplinary action against Greece is not expected until December.