Tsakalotos, who recently replaced pugnacious negotiator Yanis Varofakis, apparently prepared his case with Sapin ahead of the 3.00pm meeting with all the Eurogroup's finance ministers.
Earlier, sources confirmed reports that French leaders, including President François Hollande, had been working hard to avoid a Grexit, sending civil servants to help prepare Athens's latest proposals to the creditors, which were passed by the Greek parliament on Friday.
"The idea is not to dictate to the Greeks what to write but to give them advice that would allow them to propose reforms that would be acceptable to the International Monetary Fund and the European Council," a French official told Le Monde newspaper.
The government has not officially confirmed the reports.
Hollande and other French leaders on Friday declared the Greek proposals "serious" and "credible".
They appeared very keen that agreement should be reached over the weekend.
The French attitude contrasts with that of the German government and the Greek crisis has seen divisions appear in the habitual unity between the European Union's two leading nations.
"Since the beginning of negotiations in June, observers of the [European] Commission have noticed several times that documents presented by Athens in working meetings were similar to those presented by Paris on several points, comments Le Monde.
Analysts told the AFP news agency that a deal would be a "triumph" for France and specifically for Hollande, who is struggling with poor poll ratings at home.
The president is reported to have spent hours on the phone with Tsipras and Commission president Jean-Claude Juncker this week.
Part of this could be enlightened self-interest, if Varofakis is to be believed.
"Based on months of negotiation, my conviction is that the German Finance Minister [Wolfgang Schaeuble] wants Greece to be pushed out of the single currency to put the fear of God into the French and have them accept his model of a disciplinarian eurozone," he wrote in the British paper The Guardian on Friday.