Henry Kravis’ KKR on Sunday was close to a deal to buy Envision Healthcare for about $5.5 billion, according to a report.

The $46 a share deal could be announced as soon as Monday.

The Post on June 4 was the first to report that KKR had made a final offer for the Tennessee company and had arranged financing equal to 7.25 times Envision’s earning before interest, taxes, interest and depreciation — a hefty sum.

The probable deal, with a value of about $10 billion including debt, would be the largest in the last several years, according to The Wall Street Journal, which reported the imminent transaction.

The $46 sale price represents a 5 percent premium over Friday’s close of $43.64 — but 56 percent over the stock price on Nov. 1, a day after it said it hired advisers and said it would explore its options.

At the time, the company was rocked by disappointing third- quarter results.

Two other bidding teams were also interested in Envision, including a partnership between Carlyle Group and TPG Capital, The Post reported earlier this month.

Envision supplies doctors to hospital emergency rooms.