A deal could be announced as soon as Monday, the source said.

A KKR spokeswoman declined to comment. Envision did not respond to a request for comment outside regular business hours.

The agreement will come less than two weeks after KKR said it will buy U.S. business software company BMC Software in a deal which sources valued at $8.5 billion, including debt, making it the buyout firm's largest acquisition since the 2008 financial crisis.

Reuters reported last month that KKR and U.S. hospital operator HCA Healthcare Inc had joined forces to make an offer for Envision, with the move aimed at giving HCA and KKR an edge over buyout firms, which were also pursuing Envision.

Other private equity firms competing for Envision included a consortium of Carlyle Group LP and TPG Global, sources told Reuters in May.

Envision said in 2017 that it was reviewing a range of strategic alternatives after reporting disappointing third-quarter earnings, which were attributed partly to the impacts of hurricanes Harvey and Irma, along with a slowdown in the growth of patient demand.

The Wall Street Journal had earlier reported that KKR is nearing a deal to buy Envision.

KKR had agreed last month to acquire BMC from private equity companies Bain Capital and Golden Gate Capital, which bought BMC for $6.9 billion in 2013.

KKR had a successful year for fundraising in 2017, with the private equity firm's fund closings including a $13.9 billion North America private equity fund and a $1.45 billion healthcare fund.

(Reporting by Liana Baker in New York and Kanishka Singh in Bengaluru; additional reporting by Joshua Franklin in New York; Editing by Lisa Shumaker)

By Liana B. Baker and Kanishka Singh