Finance Minister Michael Noonan says he believes Greece has a "better than 50 per cent" chance of agreeing a new bailout deal.
Prime Minister Alexis Tsipras has promised to put forward "credible" proposals to reforms its economy today, in a bid to get the bailout deal he wants.
However, no agreement is expected before an EU leaders summit on Sunday.
Speaking to The Pat Kenny Show on Newstalk, Mr Noonan said the Greek government seem more serious about getting a deal after Sunday's referendum and he expects they will.
"It's a better than 50 per cent (chance).
"What has changed is, a lot of us around the table weren't sure is they were serious about making a deal or if they wanted to leave the Euro and blame the European institutions for forcing them out.
"It seems now they are quite serious and the have started the legal process.
"We got a letter signed by the Prime Minister of Greece, on behalf of his government and the Greek people, requesting a third programme for Greece."
"Very impressive"
Greek's new Finance Minster, Euclid Tsakalotos, is "very impressive", Mr Noonan said. Pat Kenny asked Mr Noonan if the former Greek Finance Minster Yanis Varoufakis had been engaging in tactics rooted in game theory, on which he is an expert.
"I really don't know," Mr Noonan said. "If he was he didn't win."
Varoufakis, who stepped down following last Sunday's referendum in Greece, "certainly didn’t make a big effort to inspire the trust and confidence of his colleagues around the table.”
There has been a charge in recent days that Noonan has been excessively harsh on Greece as it bargains for a new deal. “I want Greece to stay in the eurozone," he said. "Whatever our ideological difference would be with the Greek government I have terrific sympathy with the Greek people.”
USC cuts
On the domestic front, Mr Noonan said in Budget 2016 he is “going to cut personal taxes. I’m going to cut USC by at least 1 per cent maybe more ,” with the aim of ensuring “work pays better” and encourages people back into the workforce.
In April, the Department of Finance in its Economic Statement projected that because of the strength of the economic recovery and booming tax revenue receipts, it had room for a give-away budget of €1.2bn to €1.5bn.
In a wide ranging extended interview Mr Noonan also discussed mortgage rates, NAMA, Brian Cowen at the Banking Inquiry and the next General Election.