Merkel is due to hold a press conference on Monday.
Speaking at a Monday briefing, the key Merkel ally and Christian Social Union (CSU) party head said that the chancellor effectively approved nearly all provisions of his so-called "master plan".
The regulations have already admitted more than one million migrants into Germany, who are then allowed to travel to other European Union member states without restriction.
In Brussels, the European Union asylum office said Monday the number of people applying for global protection in Europe plunged past year but remains higher than before 2015, when more than 1 million migrants entered, many fleeing the war in Syria.
Top CSU leaders huddled Monday morning in the party's home base of Munich. Seehofer has said these migrants should be turned away at the German border whereas Merkel has said this can only happen with the agreement of the relevant European Union states.
Striking a conciliatory tone in a guest column in the Frankfurter Allgemeine paper, Seehofer said the cohesion of Europe and Germany was at stake.
"The situation is serious but still solvable", he wrote.
Merkel wants two weeks to try to strike bilateral deals with partners, such as Italy and Greece, on migrants - possibly similar to one struck between the European Union and Turkey in 2016 - and to make progress at a June 28-29 European Union summit on an EU-wide policy. CSU leaders had previously been dismissive of her chances to reach agreement there, given that the issue has bedeviled the continent for the past three years, with no resolution in sight.
Migration, always a fraught political issue for Europe, has become even more sensitive in recent weeks. This is causing friction not only between governments but inside them as well.
Austria, governed by a center-right and far-right coalition, has also vowed to take a much tougher stand.
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The day's action also pits another scrappy underdog against one of the favourites in Group C when Australia play France . The opposition is going to give us more respect than they did in the past, though.
US President Donald Trump has launched another attack on one of America's allies, this time, Germany is his target as he tweeted "the people of Germany are turning against their leadership as migration is rocking the already tenuous Berlin coalition".
Speaking about the possibility of Angela Merkel and Emmanuel Macron finalising an agreement, the source said: "There will be no agreement if there isn't a general agreement on all parts of the proposal".
The signs of splintering Republican support come after longtime Trump ally, the Rev. Franklin Graham, called the policy "disgraceful".
Merkel argues that Germany must not take the sudden and unilateral step of rejecting asylum seekers at the border, which would add to the burden faced by frontline countries like Italy and Greece.
But the veteran politicians have often clashed.
Instead, she wants to find a common European solution at the June 28-29 EU summit.
Merkel is locked in a standoff with her interior minister, Horst Seehofer, over his demand for some asylum-seekers to be turned back at the border. "Germany is characterized by Christianity".
It wasn't immediately clear what she might offer other countries in talks. The CSU fears electoral disaster in upcoming regional elections.
With an eye on October's Bavaria state election, the CSU is anxious to assure voters that it has a roadmap to curb the migrant influx.
The CSU appeared to be at pains at the weekend to limit the damage done to the conservative alliance amid growing evidence the German government could be about to collapse.
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