VIENNA (Reuters) - The chances for a third bailout program for Greece are improving, Austrian Chancellor Werner Faymann told newspaper Oesterreich in an interview to be published on Sunday.

"We are certainly closer to a deal than we were earlier. I would even say the chances for an agreement for a Greece bailout program have never been so good as they are now," he said.

"However, we are still far from a final yes for the bailout because some countries have lost trust in Greece."

Skeptical European finance ministers were gathering on Saturday to decide whether to negotiate a third bailout for Greece after Prime Minister Alexis Tsipras won lawmakers' backing for painful austerity measures.

Faymann said Greece would have to improve its offer because it now needed more than the originally named 53 billion euros ($59 billion).

He said again: "We must avoid a Grexit - that would set Europe back. So we must seek a constructive solution."

Faymann said such a solution would not mean a haircut for creditors but a reduction of the interest burden by giving Greece longer to pay back its debt.

(Reporting by Georgina Prodhan; Editing by Hugh Lawson)