Quoting "several" sources with knowledge about the deal, the newspaper said that Signa, the holding company of Austrian real estate magnate Rene Benko, has completed a review of Kaufhof's accounts and submitted a written offer.
And that offer was discussed by Metro's supervisory board at the beginning of May, it added.
Benko has already tried unsuccessfully to buy Kaufhof in the past.
Kaufhof has around 120 department stores in Germany and 16 in Belgium where it operates under the Galeria Inno brand.
It has annual sales of around €3.0 billion and employs a workforce of 21,500.