Generali gained 2.5% in Milan to change hands at €15.84 each, extending their three day gain to 15% and valuing the group at just under €25 billion.
Intesa said late Tuesday that, in accordance to its current business plan, it "will examine any possible opportunities to strengthen its competitive positioning and, therefore, the Group's future financial performance."
"These opportunities, including possible industrial combinations with Assicurazioni Generali, are currently being examined by the Bank's management," the statement added.
Reuters also reported that two of the banks main shareholders -- Compagnia di San Paolo and Fondazione Cariplo -- would support a Generali takeover.
Anti-trust issues, however, could thwart a potential tie-up and authorities in both Rome and Brussels would closely examine any tie that combines the country's second-largest lender and its biggest insurance group. Bloomberg reported Wednesday that Consob, the country's stock market regulator, is gathering information on the developments.
Media speculation over the weekend linked Intesa and Germany's Allianz (AZSEY) , Europe's biggest insurer, to a planned takeover of Generali which would split the company's assets.
Neither party has commented on the reports, although now that Generali has a 3.01% stake in Intesa, Italian laws on cross-shareholding forbid Intesa from owning any more than 3% of Italy's biggest insurance company without making a formal offer for at least 60% of the company.
Intesas shares were marked 2.88% lower in Milan at €2.23 each. Shares in Allianz were modestly higher in Frankfurt, rising 0.13% to €158 each.