Discussions have been taking place for months, according to several people briefed on the negotiations, but they slowed in recent weeks during Italy's political crisis.
Any deal would solidify BlackRock's standing and further disrupt the continental European market, which is tightly controlled by domestic banks and insurers.
The thrust of the talks has been over a distribution arrangement between the two. Tommasso Corcos, chief executive of Eurizon, has stated he would sell up to a fifth of the business and that he wanted to conclude a deal by the end of the year. BlackRock, which manages $6.3tn globally, is understood to be seeking a 10 percent stake. Financial terms have yet to be agreed.
On behalf of its clients, BlackRock holds 5 percent of Intesa Sanpaolo, which owns Eurizon, making it the Italian lender's second-biggest shareholder.
The New York-based manager is keen to gain more influence in Italy, which is dominated by distribution networks operated by banks and insurers.
Eurizon, meanwhile, hopes to leverage a relationship with a global asset manager to gain access to clients worldwide.
Last year Larry Fink, BlackRock chief executive, said he expected the mergers and acquisition wave in asset management to continue, but said his company would restrict itself to smaller deals.
It has since taken a minority stake in UK robo-adviser Scalable Capital, acquired $9bn alternatives manager Tennenbaum Capital Partners and bought Cachematrix, a financial technology provider. It has also acquired the asset management division of Citibanamex, Citigroup's Mexican operation.
BlackRock has expanded aggressively in Europe over the past decade and is the region's largest manager by assets. The $1.8bn it oversees in Europe represents 28 percent of the company's total and provides 30 percent of its revenue. In Italy, it is the fifth largest wealth manager, with a 4 percent market share.
Carlo Messina, Intesa chief executive, told the Financial Times in April that the bank was looking for a partner for Eurizon.
"We are studying the possibility to make a strategic alliance with a big player in assets under management and we are ready to also sell a minority stake in order to have a possibility to play a game of consolidation of assets under management in Europe," he said.
In 2015 Eurizon bought a 65 percent stake in SLJ Macro Partners, a UK hedge fund manager, and the two have since launched a macro fund.
BlackRock and Eurizon declined to comment.
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