CDU general secretary Annegret Kramp-Karrenbauer said earlier that party leaders were "united" behind Merkel and "effective, humane solutions together with our European partners".
A resignation would eliminate the main opponent to Merkel's key proposals for asylum reform and for further European integration.
Seehofer and Merkel, who have long had a hard relationship, have sparred over migrant policy on and off since 2015.
Knaus, director of the thinktank ESM, said the deal struck by the German government could have the unintended effect of increasing migration into Germany, if for example the Greek government used the new agreement to unite families with people who had already arrived in Germany, while in return taking back some asylum seekers who have been finger-printed in Greece.
Kurz's conservatives won last year's parliamentary election with a hard line on immigration, pledging to prevent any repeat of the 2015-2016 migration crisis in which Austria took in more than 1 percent of its population in asylum seekers and more than a million crossed its territory into Germany.
In a meeting with his party leaders on Sunday night, Seehofer offered to resign from his ministerial role and party leadership, reports said.
However, according to das Bild, Seehofer called the meeting on Saturday evening an "ineffective conversation".
The two agreed to set up three transit centers for asylum seekers on the border with Austria, confining them there as their cases are quickly processed.
In high-stakes crisis talks on Monday, Ms. Merkel put to rest for now a unsafe row with a longtime rival, Interior Minister Horst Seehofer, that had threatened the survival of her shaky 100-day-old coalition. His ultimatum forced Ms. Merkel to seek a European Union mini-summit the previous weekend and diverted the scheduled European Union summit this past weekend to an all-night crisis meeting on the migration issue.
He also believes that these elections "would revolve on the immigration issue" with no chance of victory for the Christian Democratic Union.
"The conflict has been so severe that either Angela Merkel loses face or Seehofer loses his job and Merkel loses her job as the chancellor within a few weeks", he claims.
The deal still needs the blessing of the centre-left SPD party in Merkel's coalition to go ahead.
"We have many open questions", said Nahles, whose lawmakers discussed the deal on Tuesday.
The "Union" of CDU and CSU have blended the southern state's beer-and-lederhosen-infused conservatism with more moderate politics, forming a centre-right force that dominated Germany for decades. "The German government has truly made a mountain out of a molehill", said Gerald Knaus, the architect of the 2015 migration deal between the European Union and Turkey.
"The CSU's immigration policy and its treatment to its sister party are only supported by a minority", Forsa head Manfred Güllner told the RTL/n-tv broadcaster, which commissioned the survey.