Kaczynski and his twin brother Jaroslaw, the Polish prime minister, believe the voting system enshrined in the proposed treaty gives too much power to the EU's bigger countries, Germany in particular.
'Soul of Europe'
They have threatened to block progress on the charter for reforming EU institutions at the summit to be held on June 21-22 if their demands for re-weighting the EU voting system are not taken into account.
Merkel has described her efforts to breathe life into the deadlock over the constitution as a quest to find the "soul of Europe" and said she would continue talks with European leaders ahead of the summit, which will be the last before the rotating presidency moves on from Germany.
"We will now put forward a proposal for such a schedule.
The readiness of all to compromise will be necessary for it to be adopted," Merkel said in her weekly podcast, before the meeting with Kaczynski.
Merkel is due to meet Merkel is due to meet Mirek Topolanek, the prime minister of the Czech republic, the only other country to support the Polish stance, in Meseberg on Sunday.
Poland has been subjected to a diplomatic offensive.
Jose Manuel Barroso, the head of the EU Commission, warned Warsaw against blocking the implementation of reforms for an EU that has almost doubled in size in the space of three years and cannot function with its current decision-making system.
Nicolas Sarkozy, the new president of France, visited Poland on Thursday and, on Friday, Poland held out the possibility it could drop its threat to veto treaty talks.
The deadlock over the constitution began when French and Dutch voters rejected it in referendums in 2005. Sarkozy and Jan Peter Balkenende, the Dutch prime minister, met on Saturday and largely agreed on measures to revamp the EU's institutions.
The leaders "agree to favour the solution of a simplified [EU] treaty that would not have the characteristics of a European constitution", David Martinon, Sarkozy's spokesman, said after the talks in Versailles, near Paris.