But other senior figures in his Christian Social Union party (CSU) denied that any such deal had been agreed.
The dispute broke out last week after Merkel blocked Seehofer's plans to turn away migrants who are already registered in other European Union countries at the German border.
Seehofer issued her with an ultimatum, threatening to take matters into his own hands and issue unilateral orders as Interior Minister unless she agreed to the policy by tonight.
That would have left Merkel with a choice between sacking him and risking the collapse of her Government, or suffering a potentially fatal blow to her authority.
The CSU threatened to withdraw from her coalition if Seehofer was sacked, which would have left her without a majority in Parliament.
The indications were that Seehofer may have blinked first in the stand-off. But he still has to win backing for any stay of execution at a CSU meeting tonight.
"No one in the CSU is interested in overthrowing the Chancellor or bringing down the government," Seehofer told Bild am Sonntag newspaper.
But behind closed doors he gave party colleagues a different message, according to Welt am Sonntag, telling them: "I cannot work with that woman any more".
Merkel is reportedly seeking urgent talks with key European Union allies on the frontline of the migrant crisis in an attempt to stave off the crisis.
She wants to negotiate bilateral deals with Italy, Greece and Austria to allow Germany to turn away asylum-seekers who are already registered there.
"So far nothing has been decided, we are in the planning phase. It is also unclear when exactly this special summit could take place," Bild quoted an unnamed Italian Government source as saying.
A spokesman for Merkel said there were currently no official plans for a special summit but added: ""It goes without saying that the federal Government is holding talks with different Member States and the European Commission on this".
Merkel's supporters say she blocked Seehofer's plans over fears they could derail her hopes of securing an Europe-wide migrant policy at the EU summit.
Merkel's Christian Democrat party (CDU) was reported to be drawing up contingency plans to seek a new coalition partner in the event of a CSU withdrawal, with the pro-business Free Democrats (FDP) and the Green Party as candidates.
There is also talk in CDU circles of running candidates against the CSU for the first time in Bavarian regional elections in October, which could split the conservative vote and end the CSU's grip on power in the state.
The manoeuvring in Berlin came as ships carrying more than 600 mirgants rescued from the Mediterranean and refused permission to land in Italy and Malta arrived in Valencia after the Spanish Government offered to take them in.
