The Greek government is widely expected to return to the bond market soon although Athens isn't saying much as it reportedly appoints banks to manage the fund raising.
"We are not commenting on how and when we might tap markets again," a spokesperson for the Greek government told CNBC on Thursday, adding that it is "examining the situation very carefully."
The Greek Debt Management Agency, which is responsible for preparing Greece's comeback to markets, refused to comment on the issue when contacted by CNBC on Thursday.
According to Reuters, Greece's debt agency has mandated six banks - Bank of America Merrill Lynch, BNP Paribas, Citigroup, Deutsche Bank, Goldman Sachs and HSBC, for a five-year bond sale. The banks declined to comment on the issue.
The topic is sensitive because it will mark the first Greek bond sale since 2014. The government is keen to go ahead with the issuance to show that the current bailout program is working and thus increasing the chances of a "clean break" from the financial rescue.
However, getting the timing right is crucial. "Going back to the markets early is a big mistake. Greece will have to pay a risk premium of several hundreds of basis points for medium term funding. All the private funding that Greece might find now will mature well before the European loans," Daniel Gros, director of the Centre for European Policy Studies, told CNBC last week.
A source close to the situation, who preferred to remain anonymous due to the sensitive nature of the issue, told CNBC Tuesday that Greece's market return is "most likely next week as the Greeks seem to prefer to wait for the IMF's EB (International Monetary Fund Executive Board) meeting on Thursday and for (credit rating agency) S&P to make announcements regarding Greece's debt rating on Friday."
Members of the IMF's executive board are due to meet Thursday afternoon to discuss issues related to the Greek bailout, including the sustainability of its debt. The Fund's opinion on the Greek bailout is crucial given that it's promised to contribute to the financial rescue, although it hasn't yet said by how much. The IMF has also been a vocal supporter of making Greece's debt more sustainable.
The opinion of S&P will also be important for market participants. The rating agency confirmed to CNBC on Tuesday that it's going to discuss the situation of Greece on Friday but for regulatory reasons it cannot unveil whether there will be a rating upgrade.
Last week, Moody's noted that credit metrics have improved for Greece with economic growth and public finances on a more sustainable path. "The recent upgrade and positive outlook on Greece's sovereign rating reflect our view that the prospects for a successful conclusion of Greece's third adjustment program have improved," Kathrin Muehlbronner, senior vice president at Moody's, said in a statement.
Greek bonds have rallied to post-crisis levels this week as investors have become more confident on the economy and the prospects of a market return.
"There are basically two reasons for this," Jan Randolph, director of IHS Markit sovereign risk rating, told CNBC Tuesday.
"Greece has been performing better than to plan, with the fiscal adjustment stronger than expected … This together with some resumption of modest growth is expected to turn debt dynamics positive; with many rating agencies (including IHS Markit) moving Greece's sovereign ratings slowly away from a possible default scenario."
"Secondly, Greece has secured another bailout program extension in June, with IMF involvement despite difference with other euro zone partners on the nature and degree of debt relief."
In June, the euro zone approved a new disbursement of 8.5 billion euros ($9.2 billion) which allows Greece to comply with summer payments to creditors.