SoftBank shares climbed 1 percent on Thursday, in line with the broader market.
SoftBank, which has declined to comment on the possible deal, has been engaged in aggressive spending over the past year.
The company said discussions are at a "very early stage" and added: "There is no certainty that any transaction will be agreed, nor as to the terms, timing, or form of any transaction".
SoftBank could purchase as much as a third of Swiss Re, one of the world's largest reinsurers, according to people familiar with the discussions, who asked not to be identified because no agreement has been reached.
"Yesterday's announcement is totally surprising as most major combinations in the reinsurance/commercial insurance space were among industry players", Daniel Bischof, an analyst with Baader Helvea AG in Zurich, said in a note to clients.
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Another route for SoftBank to take a stake in Swiss Re would be for the Swiss company to sell some of the 23 million treasury shares it holds. ("SoftBank") regarding a potential minority investment in Swiss Re. "Float" - the amount of insurance premiums collected before claims are paid - can be used as cheap funding by insurers, making them attractive to investors.
The reinsurer's shares closed at 90.18 Swiss francs on Wednesday.
Softbank's CEO, Masayoshi Son, recently said the investments are part of his plans to secure the long-term growth and health of Softbank for the "next 300 years".
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The purchase of a stake in Swiss Re would be the latest in a constant stream of investments that have made valuing SoftBank hard and left a "conglomerate discount" weighing on its share price.