Negotiators said there were "encouraging" signs from meetings over the weekend in Brussels on reforms which Athens must push through in exchange for 7.2 billion euros (USD 8 billion) in desperately-needed bailout funds.
The talks, which began Thursday, were the first led by economist and junior foreign minister Euclid Tsakalotos, who last week replaced the controversial Varoufakis as head of Greece's team of negotiators.
After months of acrimonious deadlock, "the revamped (Greek) Brussels group have clearly improved the process, with a clear schedule for the discussions... And with more experts present with more details," one source said.
Varoufakis had a notoriously difficult relationship with his country's lenders, and was reportedly "isolated" by his fellow European finance ministers after a stormy meeting in Riga two weeks ago.
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A second EU source confirmed there had been "convergence on some issues" during talks over the weekend, though "more work was needed on others" when the teams sit down again on Monday.
Greece's semi-official ANA news agency also reported progress and an improved atmosphere in talks.
"Yes, I'm in charge. I'm still responsible for the talks with the Eurogroup," he told the weekly Die Zeit on Thursday.
"I'm supported by various government members, not least by good friend Euclid Tsakalotos. The fact that some media are portraying as if he is replacing me in the talks is just another proof of how low journalistic standards have sunk," he said.
Discussions between Athens and its creditors are hung up in particular on cuts to pensions and deregulation of the labour market, a difficult pill to swallow for Prime Minister Alexis Tsipras's radical government that was elected four months ago promising to end years of austerity that has ravaged the economy.