Merkel and Seehofer are due to speak to the press at 2 p.m. local time.
Joachim Herrmann, Bavaria's interior minister, insisted the CSU was not intending to destabilise the CDU.
Merkel's junior coalition partner - the Bavarian Christian Social Union (CSU) - is under pressure from the nationalist Alternative for Germany (AfD) party, which became Germany's largest opposition party in the elections a few months ago. Still, polls suggest that its absolute majority in the Bavarian state legislature is in danger in the October 14 state election and it is being challenged on the right by the far-right, anti-immigrant Alternative for Germany party.
At a meeting of his party's leadership in Munich on Monday, Seehofer suggested the plan could be introduced piecemeal, in order to avoid pre-empting Merkel's negotiations in Brussels.
Chancellor Angela Merkel's fourth-term government took almost six months to put together, taking office in March after the center-left Social Democrats reluctantly agreed to team up with her conservatives again.
Seehofer on Monday agreed to implement his immigration "master plan" step by step, stopping short of unilaterally enforcing a policy opposed by Merkel while she attempts to find a solution at European level, sources have told German news agency DPA.
"The overwhelming majority of the German population supports this idea" - of turning the previously registered back at the borders - "and that's why we want to provide support today for implementing it", he said.
Mr Seehofer told Bild am Sonntag newspaper: 'No one in the CSU has an interest in bringing down the chancellor, to break up the CDU/CSU parliamentary alliance or to blow up the coalition. 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.
Led coalition bombed Syrian military base in Dayr al-Zawr
Asked about the reported air strikes, an Israeli military spokeswoman said: "We do not comment on foreign reports". The Syrian Observatory for Human Rights reports that 40 pro-Assad regime fighters were killed in the strike.
If Merkel is given a two-week ultimatum, she would still face the challenge of persuading European Union governments to sign up to a common plan on the migrants.
The row boiled over this week when a boat carrying Libyan migrants rescued at sea was refused permission to dock on either Italy or Malta.
Seehofer and Merkel have long had an awkward relationship.
Later in the day, she will host the new Italian Prime Minister, Giuseppe Conte, who is heading a government with an anti-immigration agenda.
Austria, governed by a center-right and far-right coalition, has also vowed to take a much tougher stand. However, Merkel has been unyielding in defending her initial decision to keep Germany's borders open, telling lawmakers earlier this month that "in an exceptional humanitarian situation, Germany behaved very responsibly".
At the centre of the showdown between Merkel and Seehofer, who are bitter rivals after the chancellor's decision to allow nearly a million refugees into Germany three summers ago, is disagreement over whether to allow those who have already registered in another European Union country entry to Germany.
The reference to the summit is significant; Merkel has indicated she plans to push her fellow European leaders for a new approach to asylum when they meet late next week. However, the CSU's General Secretary denied the report. Merkel said she would first present the results of the talks to her own party on July 1 and then discuss them with her Bavarian allies.