Allianz and Commerzbank, Germany's second-biggest bank, may call supervisory board meetings by this weekend to discuss the sale, said the people, who declined to be identified because the talks are private.
A deal may value Frankfurt-based Dresdner at as much as 9 billion euro ($13.2 billion), analysts estimate.
Allianz, which bought the bank for 23.5 billion euro in 2001, put it up for sale this year after subprime-related losses at the Dresdner Kleinwort securities unit eroded profit. While Commerzbank is the preferred suitor, the Munich-based insurer is also in discussions with the state-owned China Development Bank, people involved in the talks said.
"Investors are waiting for a solution for Dresdner, so a sale would be positive even though Allianz waited too long," said Lutz Roehmeyer, who helps manage about $20.5 billion at Landesbank Berlin Investment, including Allianz and Commerzbank shares. "Allianz shouldn't hesitate to accept a price of around 9 billion euro."
Allianz fell 0.9% to 109.32 euro by 10:43 am in Frankfurt trading, bringing declines this year to 26%. Commerzbank slipped 0.4% to 19.87 euro, giving the lender a market value of 13.1 billion euro.
Spokesmen at Commerzbank, Dresdner and Allianz declined to comment.