The first unofficial contacts have already been made between the two rival German banks, the paper reported, citing financial sources.
A person with knowledge of the matter also confirmed the report to Reuters news agency, adding that talks are at a very early stage and could fall apart.
Spokespeople from both banks declined to comment on the reports on Saturday.
Pressure from German government
The latest development in the "will they, won't they" saga between the two major German financial institutions has come amid increased pressure from Berlin.
The German government, which is Commerzbank's largest shareholder, wants the two sides to make a decision in the coming weeks, Welt am Sonntag reported.
The German government wants a decision before the European Parliament elections in May, which could see a possible change in power that could block the move — or thwart state help the two banks might need during the merger, the paper reported.
A Finance Ministry spokesperson declined to comment on the report, but in the past Finance Minister Olaf Scholz, who has emphasised the importance of strong banks.
Read more: Opinion — What's to become of Deutsche Bank?
Concerns over merger
Supporters of a merger say that this could possibly be the last chance to strengthen the German banking sector and possibly thwart the likelihood of Commerzbank being taken over by a foreign buyer.
The combined entity would have an estimated equity market value of over €24 billion ($27 billion) and would comprise a 20 percent share of the German retail banking market, according to Reuters.
Labor unions have opposed a possible merger, saying it could lead to major job losses. Others also believe a merger would allow the two to charge higher prices in Germany where banking services have been either low cost or free.
Deutsche Bank, a global investment giant and Germany's largest lender, has been plagued by money laundering scandals and the fall-out from the financial crisis, with the bank's shares falling by 73 percent over the past five years.
The German government has held a 15 percent stake in Commerzbank after bailing out the financial institution out during the financial crisis. The bank has, however, seen its stock price fall to the point where it's no longer listed in Germany's index of top 30 publically traded companies.
rs/sms (dpa, Reuters)