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.
It was the latest aftershock from Merkel's 2015 decision to open Germany's borders to more than a million refugees from war in the Middle East and Africa.
"The sum total of everything we have agreed upon has the same effect" as what Seehofer has demanded, Merkel said in an interview with ZDF television, as reported by AP.
But according to reports from a crunch party leadership meeting in Munich that stretched into early Monday morning, other party leaders were trying to dissuade Seehofer from stepping down.
"We want on the one hand to set up transit centres in Germany and from there carry out returns in agreement with countries from which asylum seekers come and where they are already registered", Mrs Merkel told reporters.
Leaders from both Mr Seehofer's CSU and Merkel's Christian Democrats spent tonight in crunch talks, attempting to settle an increasingly personal row that threatens to bring down her three-month-old government.
If Seehofer does quit, the CSU could offer a replacement interior minister if it aims to remain tied to Merkel's CDU party.
The political crisis is one more sign of a growing rift in Europe between those who want to work together to reduce the number of migrants and refugees entering the bloc, and those who have grown exhausted of failed attempts to reach bloc-wide agreements and are taking unilateral action.
But Ms. Merkel has rejected any unilateral action by Germany, and insists on a coordinated European approach, as agreed at last week's EU asylum-policy summit in Brussels.
The disagreements reached a peak this weekend when Merkel's party passed a motion supporting the immigration deal she negotiated with European leaders last week.
The differing opinions of the CSU - one of the main supporters of the government - and Merkel's party, the Christian Democrats (CDU), has raised several questions regarding the weight of the leadership of the German Chancellor.
Other parties and the media have slammed what they call a reckless game of chicken, with Der Spiegel commenting: "It is fair to ask: has the CSU lost its mind?"
The compromise also needs to be approved by Merkel's other coalition partner: Germany's Social Democratic Party (SDP), which might chafe at the notion of any sort of migrant centers or camps along the border with Austria but which also stands to lose in any round of new elections that might be triggered by rejecting the compromise.
Seehofer, who reportedly argues that measures to tackle migration agreed at an European Union summit last week aren't enough, said early Monday he would hold talks during the day with the CDU.
He has threatened to turn away some categories of asylum seekers at the German border while Mrs Merkel has sought a European solution.
Austria's Vice Chancellor Heinz-Christian Strache of the far-right Freedom Party warned last week that on the day Germany sends back migrants "we will be ready and secure our own borders".