Swiss Re's shares last traded at 90.18 Swiss francs, giving it a market capitalisation of 31.51 billion francs ($34 billion).
SoftBank, which has declined to comment on the possible deal, has been engaged in aggressive spending over the past year.
Japanese conglomerate Softbank is in preliminary talks to acquire minority stake in reinsurance giant Swiss Re.
It would also come at a time when the reinsurance industry has been hit by rock bottom interest rates that have dampened investment returns with falling industry prices putting pressure on margins.
SoftBank has made other investments the insurance industry, and has stakes in Chinese online insurer ZhongAn, health insurance claim processing service Ping An HealthKonnect set up by Ping An Insurance Group, and US insurance startup Lemonade.
Analysts said SoftBank could be attracted by Swiss Re's research capabilities and undervalued stock, while the company's cash generation could prove attractive. The billionaire has been racking up a dizzying array of investments over the past year as he reshapes Japan's largest mobile-phone carrier and majority owner of Sprint Corp. into a force in the technology world. Buffett has used the "float" - or premiums held by such businesses before paying claims - to fuel his stock picks and acquisitions at Berkshire Hathaway Inc.
"SBG is now accelerating its global investment activities through the SoftBank Vision Fund and other vehicles to drive overall growth for the SoftBank Group", said the Japanese firm.
Swiss Re's top management recently visited Japan and met with SoftBank Chairman and CEO Masayoshi Son, the report said.
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