"They agreed that the prime minister will present the proposals at the eurozone summit," the source told AFP news agency.
Tsipras has been frantically working phones at his desk in Athens following the Greek people's "No" vote in the referendum on new bailout conditions from its creditors , calling European Central Bank (ECB) head Mario Draghi and Russian President Vladimir Putin on Monday.
Greek President Prokopis Pavlopoulos also rang French President Francois Hollande.
Meanwhile, Vice-Chancellor Sigmar Gabriel told journalists in Berlin that the referendum result was a breach of eurozone rules.
But he added that other eurozone countries should stand ready to help Greece with humanitarian aid.
"The people there need help and we should not refuse it because of the result of the referendum," he said.
German government spokesmen had said in a press conference earlier on Monday that it was up to the Greek government to make new proposals following voters' rejection of the latest bailout offer from creditors, but insisted that debt relief was out of the question.
At a government press conference in Berlin, Merkel spokesman Steffen Seibert insisted that Greece must make the first move.
But he maintained that despite the crisis, the German government was still focused on keeping Greece inside the single currency.
Meanwhile, Finance Ministry spokesman Martin Jäger said that Germany would not accept any cut in Greece's debt.
Germany has something of a vested interest in this question as the largest holder of Greek debt:
Merkel heads to Paris
Chancellor Angela Merkel had discussed the outcome of Greece's referendum with French President Francois Hollande in a telephone call Sunday evening, with both agreeing the 'No' vote must be respected, a German government spokesman said.
"Both were in agreement that the vote by the Greek people be respected. The Chancellor and the President are in favour of calling for a summit of eurozone heads of state and government heads on Tuesday," the spokesman said.
On Monday Merkel spokesman Steffen Seibert added that Germany saw France as a key partner in the crisis and the two leaders would be discussing the referendum result over dinner in Paris.
The two leaders had sent a corresponding request to do the president of the European Council, Donald Tusk, according to sources in the French presidency.
There are no explicit provisions in EU rules for summits of eurozone leaders, but they can be held in exceptional circumstances. The last such summit was held in Brussels last month.
Official results from close to 90 of Greece's polling stations showed more than 61 percent of Greeks had voted 'No' to creditor demands for further austerity in return for further bailout funds.
"The talks with the French president from 630 p.m. (1230 EDT), and over dinner will be about a common assessment of the situation after the Greek referendum and the continuation of the close German-French cooperation on this subject," said Seibert.
Torn down bridges
Greek Prime Minister Alexis Tspiras has "torn down the bridges" between Greece and Europe, making new negotiations
"difficult to imagine" after the apparent 'No' vote in the Greek referendum, deputy chancellor Sigmar Gabriel said on Sunday.
Tsipras and his government are taking Greece down a path of "bitter renunciation and hopelessness," Gabriel told the Tagesspiegel in the first high-level reaction from the German government.
Tsipras has "torn down the last bridges which Europe and Greece could have crossed to find a compromise," said Gabriel, who heads the centre-left Social Democratic Party that shares power with Chancellor Angela Merkel's conservative Christian Democrats.
"By saying 'No' to the eurozone's rules ... negotiations over billions of euros in bailout programmes are difficult to imagine," Gabriel said.
Another SPD official, Michael Roth, who is state minister for Europe in the foreign ministry, said the resounding 'No' vote would not make things easier for Europe, and least of all the Greeks themselves.
"Whoever is cheering now, hasn't understood the seriousness of the situation," Roth wrote on Twitter.
"Nothing is going to be easier. Least of all for Greek men and women," Roth warned.
In a first reaction from Merkel's CDU party, deputy party chief Julia Klöckner warned that Tsipras should not believe he could use the referendum's outcome to pressure Europe into a better deal.
"The Greek government used anti-European propaganda and distorted messages in their campaign for a 'No'," Klöckner said.
"But it's not only the will of the Greek people that counts, but also the citizens of other European countries. Mr. Tsipras should not believe that he can use this referendum to put pressure on Germany and the European partners.
The EU is not a union where you can simply wish for whatever you want, where some members can individually determine the rules of play while the others pick up the tab," she said.