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Greece has submitted a new reform plan to its international creditors, a European official told CNBC Tuesday, as hopes of a deal pushed Greek shares as much as 2 percent higher.

It comes after months of gridlock between indebted Greece and the bodies overseeing its bailout program -- the European Commission, European Central Bank (ECB) and International Monetary Fund (IMF).

Greece is rapidly running out of money and has not yet received the last tranche of aid from its current bailout program because it has not implemented reforms that are a condition of the aid.

But a source, who did not want to be named due to the sensitive nature of the discussions, told CNBC that Greece had now submitted a reform plan made up of two documents.

"Greece has submitted two papers (to its creditors)," the European official told CNBC, confirming an earlier report by AFP.

One set of proposals concerns concrete measures, fiscal targets and the conclusion of the bailout review, the official said, and the other is on debt and financing Greece when its current bailout program comes to an end in June.

The benchmark Athens Composite index jumped over 2 percent in early Tuesday trade. It pared gains during the session to close around 0.6 percent higher, outperforming all other major European bourses.

Greece's lenders have also discussed an extension to the country's bailout program, the source confirmed to CNBC, adding that it was just one possibility.

However they said a six-month extension to the program -- as first reported by the Wall Street Journal -- was unlikely to be accepted by other euro zone member states.

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"I think many would rather support a three-month extension," the sources added.

Compromise coming?

Any extension to prolong the country's bailout program (which was already extended in February by four months) could be seen as an attempt to break the current impasse over reforms between Greece and its creditors and avert a Greek default.

Greek government sources told CNBC that the country was working on a compromise that would be made public on Wednesday at a summit with German Chancellor Angela Merkel and French President Francois Hollande.

The sources, who also asked not to be identified because of the sensitivity of the situation, would not confirm the sending of new proposals to creditors, however.

Read MoreGreece: Leaders lash out as tempers fray

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But there are concerns that a bailout extension would simply postpone Greece's economic problems.

Philippe Waechter, head of economic research at Natixis Asset Management, told CNBC Monday that a solution was needed now -- not next March.

"It's bringing uncertainty to the European markets, and not only in Europe – I was in Asia last week and the main topic for them is Greece. We need to find a solution rapidly, not waiting until next year," Waechter told CNBC Europe's "Squawk Box."

"We all need a solution on this issue because Greece is a small country in Europe, but its behavior is conditioning all the current situations in the euro zone and that's not sustainable."

- By CNBC's Holly Ellyatt, follow her on Twitter @HollyEllyatt. Follow us on Twitter: @CNBCWorld