Germany, the European Union's biggest economy, has long argued for more national competences, including over budgets, to be transferred to European institutions but faces strong resistance from other member states.
Merkel hopes a summit of EU leaders in December can agree a concrete date for the start of the convention on a new treaty, Der Spiegel reported.
The idea, which the magazine said Merkel's European affairs advisor floated at meetings in Brussels, recalls the 100-plus strong convention of EU lawmakers set up in 2001 - inspired by the Philadelphia Convention that led to the adoption of the US federal constitution - charged with the task of preparing a European constitution.
The charter that finally emerged was rejected by French and Dutch voters in 2005 and it became instead the basis of the EU's Lisbon Treaty which is still in force today.
Many member states, recalling the lengthy disputes and setbacks that preceded the Lisbon Treaty's entry into force, are reluctant to embark on another prolonged process of institutional reform.
Some countries such as Ireland would have to hold a referendum on any new treaty and the process would increase pressure in Britain - where opposition to closer EU political union runs high - for a complete withdrawal from the EU.
However, Germany believes a much closer fiscal and political union - with EU oversight of national budgets - is needed to ensure that member states get their public finances fully in order and to restore stability to the euro currency.
'I want Europe campaign'
The report by Der Spiegel comes amid signs that Angela Merkel is preparing German public opinion for a further round of European integration.
On Thursday (23 August), Merkel backed a campaign to persuade Germans of the benefits of European unity. Called "I want Europe" ("Ich will Europa"), the campaign includes a video message describing the virtues of European integration, saying it had brought "peace, prosperity and understanding with our neighbours."
"Amidst all the controversy … we must not forget one thing," Merkel said in a written statement posted on the 'Ich will Europa' website. "Europe is not just a matter of the mind, Europe is and remains primarily a matter of the heart. Europe is our future."
"I want Europe" brings together politicians past and present including the country's President Joachim Gauck, Merkel and former Chancellor Helmut Schmidt, with celebrities including German football captain Philipp Lahm, AFP reported.
It is backed by 11 academic institutes and several media groups.