The MYOB bid, if successful, would become one of KKR's biggest acquisitions in Australia and add to its 10-strong stable of technology-driven businesses in the Asia-Pacific region. KKR last year raised $9.3 billion - a regional record - in its third Asia-focused buyout fund.

MYOB disclosed the proposal in a statement and said its board was studying the non-binding offer, which was conditional on KKR obtaining financing for the deal and getting a unanimous recommendation from the target's directors.

A spokeswoman for KKR confirmed the A$3.7 per share offer for the remaining 80.1 percent of the company, and declined to comment further. The offer price, a premium of 24 percent to MYOB's last closing price, values it at A$2.18 billion.

In building its stake, KKR paid A$327 million to buy 17 percent of MYOB from its biggest shareholder, an affiliate of private equity firm Bain Capital, leaving the affiliate with a 6.1 percent stake, MYOB said.

MYOB shares soared by over a fifth to A$3.6, their highest intraday price in almost nine months, after news of the unsolicited offer. But they stayed below the KKR offer price, indicating investors did not think a higher counteroffer was on the anvil. They closed at A$3.55.

"With 19.9 percent of the register, KKR effectively own a blocking stake in the company. We think this could be enough of a deterrent for a potential interloper," JPMorgan analysts said in a note.

MYOB did not specify if Bain, which acquired the then privately owned MYOB in 2011 and listed it in 2015, was endorsing KKR's takeover offer, and a spokesman for Bain did not return calls seeking comment.

Once the dominant provider of accounting software to small and medium-sized businesses in Australia, MYOB has in recent years struggled to compete for market share with cloud-based administrative software company Xero Ltd.

Together they service more than 80 percent of the local market, according to Wilsons Equity Research, though the research also showed Xero's growth has outpaced MYOB's. Xero's market value, at around A$6.88 billion, is more than thrice MYOB's.

JPMorgan analysts said KKR's stake would make it hard for strategic investors such as Sage Group, which had attempted to buy MYOB back in 2011, and American peer Intuit Inc., maker of popular software QuickBooks, to rival KKR's bid.

An Australian-based spokeswoman for Intuit said it did not comment on market speculation. Spokespeople for Sage did not return an email seeking comment outside of office hours.

The proposed deal comes after KKR acquired U.S. business software company BMC Software in May in its largest deal since the 2008 financial crisis, underscoring how deal sizes are growing bigger again as private equity seeks to put a record $1 trillion of unused investor money to work.

For KKR, the more than A$2 billion price tag for MYOB would make it one of its largest takeovers in Australia. Its first foray in the country was a A$1.83 billion acquisition of Brambles Industries' waste management and industrial services businesses.

Last year, KKR bought Australian non-bank lender Pepper Group for about A$682 million.

(Reporting by Paulina Duran; Additional reporting by Devika Syamnath in Bengaluru; Editing by Marguerita Choy and Muralikumar Anantharaman)

By Paulina Duran