The meeting raised speculation that the political stalemate, caused by inconclusive elections three weeks ago, were nearing a solution.
But the party leaders have remained tight lipped about their talks on Thursday and Sunday.
A decision is expected on Monday after the two contenders hold a follow up meeting at 11:00am local time.
Party officials from Mr Shroeder’s Social Democrats suggest a result would only be available then.
“We will not know until midday tomorrow whether we can have
negotiations (on the coalition government),” the Social Democrats’
party chief Franz Muentefering said on Sunday.
A deal on the chancellery would pave the way for a so-called grand coalition stretching across the traditional right-left party lines, last seen in Germany in the 1960s.
A report in Focus magazine at the weekend said the most likely outcome was a government headed by Ms Merkel.
It claimed cabinet posts would be divided equally between the Social Democrats and Merkel’s centre-right Christian Democrat alliance.
Mr Schroeder has been under intense pressure to step down after the election left his party just four seats behind the conservatives.
He dismissed suggestions that his trip to Saint Petersburg on Friday to celebrate Russian President Vladimir Putin’s birthday was “a farewell visit”.
The German Chancellor has resisted calls for him to step down, seeking to show that he is not preparing to quit.
Many observers have seen his refusal to go as an audacious attempt to cling to power.
But others see him taking a gamble to ensure the best possible deal for the Social Democrats in a coalition government.
A leading member of Mr Schroeder’s outgoing centre-left administration, Interior Minister Otto Schily, renewed calls for a solution that would see him remain chancellor for two years.
Under that outcome, Ms Merkel would take over for the following two years.
“It would strengthen the necessary trust of both parties in each other and would stabilize a grand coalition,” Mr Schily told Sunday’s edition of the Frankfurter Allgemeine newspaper.
He suggested Merkel should be foreign minister to begin with, building the international contacts as she prepares for the transition.
But officials from Ms Merkel’s Christian Democratic Union (CDU) repeated their call for Mr Schroeder’s resignation.
Wolfgang Bosbach, the CDU’s parliamentary party chief, said he was concerned she would concede too much in her bid to secure the top job.
“We must be careful that we don’t end up with a Social Democrat government with Angela Merkel as chancellor,” he said.
Party leaders have warned that it could be several weeks before a government is formed.