Migrants are seen through fences as they sit on the ground in a camp near the border town of Kapciamiestis, Lithuania. AP
Seehofer told reporters the outgoing government under Chancellor Angela Merkel had "no intention" of taking such a drastic step which he said would also be "legally questionable".
In a letter to his Polish counterpart Mariusz Kaminski seen by AFP Tuesday, Seehofer proposed increasing joint patrols along its border with Poland in response to rising numbers of migrants coming via Belarus.
Seehofer said he had not yet received a response from Warsaw but praised its "very strong initiatives" to stem the flow of new arrivals.
A powerful German police union this week called for stepped-up checks at the border given the influx via Belarus, which the interior ministry said had reached around 5,700 since the start of the year.
Seehofer repeated EU accusations that the Belarusian authorities are flying migrants from the Middle East and Africa to Minsk and then sending them into the bloc on foot in retaliation for sanctions imposed over a crackdown on the opposition.
He said Merkel would be pressing the issue at a European Union summit this week.
But he stressed "the key to the solution of the problem lies in Moscow" given Russia's outsized economic and political influence on Belarus.
The surge in people crossing illegally over the EU's eastern frontier with Belarus has placed major strains on member states unaccustomed to dealing with large-scale arrivals.
Poland has drawn criticism for its hardline stance that has seen border guards push migrants back across the border with Belarus.
Seehofer said that while Berlin was concerned about the issue, it bore no comparison to the 2015-16 influx when more than one million asylum seekers arrived in Germany.