The European Central Bank told a meeting of euro zone finance ministers on Thursday that it was not sure if Greek banks, which have been suffering large daily deposit outflows, would be able to open on Monday, Reuters reported.

Officials with knowledge of the discussions, which took place at a closed-door meeting of the euro zone finance ministers and the European Central Bank and International Monetary Fund, told Reuters the deposit outflow was the only thing mentioned by ECB President Mario Draghi during his intervention.

Two officials told Reuters that during the meeting, Eurogroup chairman Jeroen Dijsselbloem asked ECB Executive Board member Benoit Coeure if Greek banks would be able to open tomorrow.

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According to Reuters' sources, Coeure answered: "Tomorrow, yes. Monday, I don't know"

The Financial Times Brussels bureau chief wrote on Twitter that the ECB denied the report on Coeire's comment. Later, the same journalist tweeted that he had confirmed the Reuters report with two senior officials who attended the meeting.

That comment was not audible during the main public meeting, a source who attended that event told CNBC—but that does not mean Coeure's statement could not have occurred in a sideline discussion.

The ECB governing council is planning to hold a telephone conference on Friday about extending emergency liquidity to Greek banks, sources told Reuters.