The holding group of Italy's Agnelli family, which also controls Fiat Chrysler, said on Sunday it was in exclusive talks to sell PartnerRe to France's Covea.
The deal could be worth around $9 billion in cash and drove shares in Exor up by more than 5% on Monday to an all-time high.
Exor, led by Agnelli scion John Elkann, bought the Bermuda-based reinsurer in 2016 for $6.9 billion after a hostile takeover battle with Axis Capital.
Analysts at Mediobanca calculated PartnerRe represents about 28% of Exor's total assets.
The source, who declined to be named, said Exor would use the cash from any ParnerRe sale mainly for acquisitions.
The cash would be in addition to the 3.6 billion euros ($3.9 billion) Elkann said last November the group would have by 2022 to spend on acquisitions.
That sum includes a planned special dividend of around 1.6 billion euros from the merger between Fiat Chrysler (FCA) and French rival Peugeot.
An analyst at Intesa Sanpaolo said on Monday the ParnerRe deal could also pave the way for a potential extraordinary pay-out to Exor shareholders, but the source said Exor planned to focus on acquisitions.
Money from a completed PartnerRe deal would only be received around the end of this year, the source said, adding the group would consider carefully before spending it.
"Exor is not a fund that needs to give a yield to subscribers every year. It wants to take time to pick the best investment options," the source said.
"It wants to avoid being offered over-priced assets simply because people know they're sitting on loads of cash".
In November, Elkann said Exor had not yet decided which sectors might interest the company, but said he saw the group "buying new companies in the future".
Besides FCA, Exor's assets include controlling stakes in luxury carmaker Ferrari, industrial vehicle manufacturer CNH Industrial and Italian Serie A soccer team Juventus.
It also has a 43% stake in publishing group The Economist.
By Giulio Piovaccari
