Swiss Re announced that it was in talks the tech-investor in February, but had never mentioned the size of the possible stake.
Financial news media including Bloomberg had cited sources familiar with the talks as saying the Japanese firm could take up to a third of Swiss Re for more than $10 billion (€8.2 billion).
At current share prices, a 10 percent stake in Swiss Re is worth approximately $3.5 billion.
In a statement released on Wednesday as the reinsurer holds an investor day, Swiss Re confirmed “that negotiations are still ongoing in respect of a minority investment by SoftBank in Swiss Re, currently expected not to exceed 10 percent of Swiss Re's share capital.”
The announcement of the talks had surprised investors, as SoftBank usually invests in technology ventures.
The company is making a concerted effort to invest in technology firms through its $100-billion Vision Fund investment vehicle.
Last year it bought a 15-percent stake in ride-sharing giant Uber — which sources said was worth $7.7 billion – while it also has piled cash into Uber's Chinese rival Didi Chuxing.
It is also the top investor in Chinese e-commerce giant Alibaba.
However, certain financial investors had noted that Swiss Re could be of interest to SoftBank as it has developed an expertise in new technologies to better understand the risks that firms active in the sector face.
Swiss Re shares fell 2.5 percent in early trading on Wednesday to 94.00 Swiss francs, while the Swiss market was down 0.3 percent overall.