An earlier bid by Santander was rejected on price, a Polish newspaper said in November.
The sale may happen in the coming weeks, the paper said.
A spokesman for Belgium-based KBC said the bank did not comment on the sale process, and Santander also declined to comment.
In October, sources told Reuters that Santander was planning to join forces with private equity firm Apax to buy KBC's stake in Kredyt Bank, worth about $1 billion.
In July, KBC said it would scrap the stalled flotations of its Czech and Hungarian subsidiaries, and would instead sell its businesses in Poland in order to repay state aid.
KBC received 7 billion euros ($9.4 billion) in state aid to help it through the global financial crisis.
(Writing By Ben Deighton; additional reporting by Sonya Dowsett in Madrid; Editing by Ruth Pitchford)