The European Commission says Greece has met the conditions to receive the second tranche of a rescue loan worth 110 billion euro ($US145 billion).
Greece has already received 20 billion euros of the loan, which was agreed by the EU and International Monetary Fund.
The Greek government has made big cuts to public spending to try to reduce the country's deficit, but economic growth has also been hit by the measures.
The Greek economy shrank by 1.5% in the second quarter of the year.
Earlier this month, the IMF said Greece had made a "strong start" to tackling its deficit.
The BBC reports finance ministers from the eurozone countries will meet in Brussels on 7 September to confirm the payment of 9 billion euros, which is due on 13 September.
The Commission said that Greece's deficit had declined by some 46%, "faster than planned", with total state cash spending reduced by 16.9% compared with the first half of 2009.
According to the latest figures from the Greek Finance Ministry, its deficit stood at 12.1 billion euros at the end of July.