"Based on the conclusions from the first review and the good progress in the second one, I think conditions are appropriate for (debt relief) discussions which must take place at the next Eurogroup", he added.
An agreement is possible by the end of the year, Moscovici told reporters at the end of a two-day visit to Athens.
Athens and its official creditors are at odds over the country's fiscal targets as well as labour and energy reforms that are part of Greece's second bailout review.
Greece's budget for next year, to be approved by parliament on Saturday next week, includes extra taxation on cars, fixed telephony, pay television, fuel, tobacco, coffee and beer. But on Tuesday, the chair of the Eurogroup of euro zone finance ministers Jeroen Dijsselbloem said European lenders "need to be realistic" over Greek fiscal targets after 2018.
Greece hopes to swiftly conclude the review and secure short-term debt relief so that its bonds are included in the ECB's bond buying scheme and it can regain market access before 2018, when its current bailout expires.
Greece and its global lenders are nearing the conclusion of the second review of the third Greek bailout program, Greek Prime Minister Alexis Tsipras and European Union (EU) Commissioner Pierre Moscovici said Monday during talks here.
Despite strong opposition by Germany, Eurogroup Chief Jeroen Dijsselbloem said debt measures would be discussed on Monday in the hopes of persuading the International Monetary Fund to sign on to the bailout.
Greece's debt will grow to 315 billion euros (US$334 billion) or about 180 percent of output this year, according to the Greek Ministry of Finance.
Eurozone ministers on Monday unlocked €1.1 billion for Greece from its huge third bailout after it delivered the necessary reforms, but held back more funds amid doubts from Germany.
European Central Bank executive Benoit Coeure has urged lenders to grant Greece relief on its massive debts, the Washington Post reports.
"All stakeholders in the Greek adjustment program realize that there are serious concerns about the sustainability of Greek public debt", Coeure told an Athens conference.
The goal is to "ultimately restore market access for Greece before the [present European Union bailout] ends in July 2018", Coeure said.