A merger between the two cooperative lenders would be the first following banking sector reforms last year aimed at spurring consolidation.
Top executives from the two banks met with regulators at the European Central Bank and the Bank of Italy on Wednesday to present their merger plan, the source said.
"The merger will be announced on the weekend of Feb 13-14 or 20-21 if the ECB clears the deal," the source said.
The tie-up is expected to be a merger of equals, the source said.
Banco Popolare is currently ranked fourth and has a market capitalisation of 2.6 billion euros.
Banca Popolare di Milano (BPM) with around 50 billion euros in assets, also has a market value of 2.6 billion euros.
Sources have said their similar market values made it easier to find an accord. BPM had also been courted by another, bigger cooperative lender, UBI Banca.