Square declined to comment to TheStreet regarding the report.
Shares of Square, San Francisco, at last check were down 8.6% to $155.32 while Intuit shares fell 3% to $315.88.
The purchase would allow Square to further build out its Cash App platform, which enables customers to send money to friends and conduct stock trading, among other functions, the Journal reported.
Intuit said in February that it would purchase Credit Karma for $7.1 billion.
"By joining forces with Credit Karma, we can create a personalized financial assistant that will help consumers find the right financial products, put more money in their pockets and provide insights and advice,” said Sasan Goodarzi, Intuit's chief executive, in a statement in February.
Credit Karma offers information on credit cards and other financial products aimed at consumers, as well as a free credit-check tool.
The site earns money by displaying personalized recommendations for financial products, such as credit cards, and collecting fees from those institutions if customers sign up.