Greece is eyeing "the current positive trend" in the market, where liquidity levels are high and there is a taste for risk-taking, the conservative Kathimerini newspaper said.
Avgi, the newspaper of the ruling Syriza party, said that Athens would "probably" test the waters as early as Monday, "even though nothing can be taken for granted."
Whether Athens will take the plunge as soon as that is unclear but the Greek government seems eager.
"It is our priority to make some test re-entry to the markets so we can prepare the ground for August 2018," government spokesman Dimitris Tzanakopoulos said on Sunday, referring to Greece's emergence from the long-running bailout programme.
"Nevertheless, the timing of this is something we are thinking over," he said in an interview with Documento newspaper.
"We want to have our first return to the bond markets at the best possible timing. I can assure you this won't happen with the goal to impress. This will be a part of our global strategy for regaining definitive access to the markets."
Greece has no immediate need to tap the bond markets for cash.