The Nikkei business daily first reported the deal, saying the investment could total up to 100 billion yen ($913 million) and give KDDI a minority stake in the online brokerage, a unit of Mitsubishi UFJ Financial Group Inc.
One of the sources told Reuters the stake would be less than 50 percent in a company valued at 127.57 billion yen as of Wednesday's closing share price.
Kabu.com's shares were untraded on Thursday with bids outpacing sell orders by nearly 20 times, likely pushing the stock to end up by the daily limit of about 20 percent. Trading resumed on Thursday afternoon after being suspended all morning.
The Nikkei said the deal would be finalised as soon as February and result in Kabu.com's likely delisting.
KDDI and Kabu.com said in statements that they were considering various possibilities but nothing had been decided. A MUFG spokesman said they had not made an announcement and nothing had been decided.
Faced with a mature market, Japan's big three telcos are looking for alternative revenue streams, with KDDI last year acquiring KidZania indoor theme park operator KCJ Group and taking a stake in price comparison site Kakaku.com Inc.
KDDI is bolstering its range of financial services, partnering Daiwa Securities Group Inc to provide asset management via smartphones. It is also in talks to raise its stake in Jibun Bank, a joint venture with MUFG's banking unit, the Nikkei also said on Thursday.
In looking to financial services to feed to large user bases, KDDI is joined by rival SoftBank Corp, messenger app operator Line Corp, and e-commerce company Rakuten Inc - which will become Japan's fourth carrier later this year.
Rakuten's entry has been welcomed by the government, which has called on carriers to slash prices to help stimulate consumer spending in other areas.
Shares of KDDI - Japan's second-largest telco by subscribers after NTT Docomo Inc - were down 0.6 percent in early afternoon trade compared with a flat benchmark Nikkei share price index <.N225>. MUFG's shares were up 0.7 percent.
($1 = 109.5400 yen)
(Reporting by Taiga Uranaka, Yoshiyasu Shida, Sam Nussey, Chang-Ran Kim and Kaori Kaneko; Editing by Richard Pullin and Christopher Cushing)