Commerzbank boss Martin Blessing and his Allianz counterpart Michael Diekmann agreed on the basic terms of a sale when they met late Thursday, the Frankfurter Allgemeine Zeitung (FAZ) and Handelsblatt dailies said on their websites.
Commerzbank, the second biggest private German bank, is now better placed than the China Development Bank (CDB), the FAZ added, even though the Chinese bank was prepared to pay more for Dresdner, which is number three in Germany.
Dresdner Bank is believed to be worth around nine billion euros.
Spokespeople at both Allianz and Commerzbank declined to comment on the reports.
A banking source told AFP however that "no decision has been made yet."
According to the reports, which cited sources close to the talks, Commerzbank would buy Dresdner in two stages, taking a 51 percent stake first in exchange for 30 percent of its own shares.
Commerzbank's board was to meet on Friday, the FAZ said, while on Sunday, the supervisory boards of Allianz and Commerzbank were expected to make their final decisions. Neither group was immediately available to comment on the reports.
A long-awaited deal would mark a significant remodelling of Germany's private banking sector, though public savings banks would continue to dominate the retail banking sector.
A combined bank would have total assets of around €1.09 trillion ($1.6 trillion) but would still trail number one Deutsche Bank, with €1.99 trillion, by a wide margin.