Schäuble's comments were reported to Deutsche Wirtschaft's Nachrichten by an MP who was present at the meeting.
The MP said that those present were surprised by Schäuble's comments as many were now working under the assumption that plans would be put in place to facilitate Greece's exit from the single currency.
Schäuble's comments come as Jeroen Dijsselbloem, the Dutch Eurogroup President, announced an extraordinary meeting of finance ministers in Brussels to be held at 7pm on Tuesday to discuss a new bailout package proposed by the Greek government on Tuesday afternoon.
Extraordinary Eurogroup teleconference tonight 19:00 Brussels time to discuss official request of Greek government received this afternoon— Jeroen Dijsselbloem (@J_Dijsselbloem) June 30, 2015
No chance of last-minute Greece deal: Merkel
Chancellor Angela Merkel said on Tuesday that there was no chance for a last-minute deal to prevent Greece defaulting on a payment to the IMF due at midnight."
This evening, at midnight central European time, the [bailout] programme runs out," Merkel said. "I don't know of any significant clues otherwise."
Europe would not cut off negotiations with Greece after the daedline, Merkel said, and the door will remain open to further discussion.
Grexit 'the best way'
On Monday and early Tuesday an increasing number of politicians in Germany were already calling for Greece to be gently ushered out of the euro.
“I believe that in the end, a cleanly prepared and reasonably organized Grexit would be the best way,” Bavarian finance minister Markus Söder said on Deutschlandfunk radio on Tuesday.
His comments followed further tough talk from federal Finance Minister Wolfgang Schäuble, who said “Greece has announced that it won't pay the IMF, that means that any future payments from the IMF will be cancelled,” on ARD public television on Monday evening.
Greek Prime Minister Alexis Tsipras had confirmed that his country would not pay the €1.6 billion due to the IMF by Tuesday in an interview on public television on Monday evening – unless there was an overnight agreement with the European creditors.
“Let them agree with our suggestions, and we'll pay tomorrow,” Tsipras said.
That prospect did not come to pass, despite Merkel's insistence in a press conference on Monday afternoon that "if anyone wants to speak with us, we are always ready to talk".
Door open a crack
But there remained voices in German politics prepared to leave the door open a crack if the Greeks would accept the Europeans' conditions.
“Once the result of the referendum is in, we will have to wait and see what Greece puts forward,” Volker Kauder, leader of the conservative CDU/CSU group in the Bundestag, said on Monday evening.
He said that there would have to be “give and take” whatever happened, “but the conditions for an aid programme haven't changed”.
Thomas Oppermann, Kauder's opposite number in the Social Democratic Party (SPD), struck a friendlier tone than his boss, vice-Chancellor Sigmar Gabriel, on Monday evening, saying that “after the referendum, of course the door will remain open”.
Gabriel had warned earlier that if the Greeks voted against the European creditors' proposals, then “no one should create the impression that the negotiations will be continued”.
Opposition Green party leader Anton Hofreiter said on Tuesday that the Greeks and Europeans should return to the table, arguing that the talks should not be allowed to fail after coming down to disagreements over €400 million.
“It can't be the case that because of that the danger of a Greek exit from the Euro increases,” Hofreiter said.