The last-ditch attempt at an agreement follows a day of drama Sunday that ended with Merkel's party rallying behind the chancellor and the migration plan she helped negotiate with fellow European Union leaders last week.
Despite Seehofer wishing Merkel "much luck" ahead of her meeting with other European Union members last week, his party has so far failed to approve the extremely vague immigration "compromise", which would ban Brussels from forcing states to set up migrant processing centers.
Mr Seehofer has threatened to turn away certain categories of asylum seekers at the country's borders, but Mrs Merkel has insisted upon a European solution.
The CSU party, facing a stiff challenge in Bavaria from the far-right Alternative for Germany (AfD) party in October's regional election, is determined to seal off its right flank.
If Seehofer does resign, it is unclear whether the CSU would seek to remain in coalition with Merkel's CDU and offer a replacement interior minister. The German leader would not comment Sunday on the outcome of the talks. With the stakes so high, senior CDU members urged the Bavarian party to pull back from its brinkmanship. "Now that the CSU is behaving more aggressively towards Merkel and the CDU, those normally critical have come to her support".
Bavarian governor Markus Soeder arrives for a board meeting on the German migration policy in Munich, southern Germany, Sunday, July 1, 2018.
It was not yet clear what effect Mr Seehofer's resignation might have.
The confrontation is over Merkel's refusal of one item in Interior Minister Horst Seehofer's 63-point so-called "masterplan" for asylum and deportations.
The CSU was meeting in Munich and Merkel's Christian Democrats in Berlin to discuss what comes next. She also would not speculate on whether she might fire him or if the issue could lead to a government confidence vote in parliament.
Merkel's Christian Democratic Union (CDU) passed a resolution on Sunday night supporting her position on migration.
But she announced after the European Union summit that she had also reached separate agreements with Spain and Greece on taking back asylum-seekers.
The EU and bilateral deals were "only possible because the chancellor enjoys respect and authority throughout Europe", Germany's EU Commissioner and CDU politician Guenther Oettinger said in an interview with the Frankfurter Allgemeine Sonntagszeitung weekly.
CDU leaders and lawmakers on Monday stressed the importance of maintaining intact the conservative alliance, Germany's strongest political force for much of its post-war history.
Political stability was upset by Merkel's 2015 decision to keep borders open to migrants and refugees arriving in Bavaria from the Middle East via the Balkans, Hungary and Austria.
Nevertheless, the anti-refugee, anti-Islam Alternative for Germany (AfD) entered parliament for the first time a year ago, leading to months of paralysis while Merkel struggled to put together a workable coalition.
Ahead of a hard Bavarian state election in October, the CSU is determined to show it is tough on migration.