The move is aimed at giving HCA and KKR an edge over buyout firms that are also pursuing Envision, which has a market capitalisation of $5.1 billion (£3.7 billion) and long-term debt of $4.6 billion, the sources said.

HCA, which has a market capitalisation of $36 billion and long-term debt of $31.6 billion, wants to acquire Envision's AmSurg ambulatory surgery business, with KKR taking the over the remainder, according to the sources.

Nashville-based Envision has asked potential acquirers to submit final offers later this month, the sources said. Other private equity firms competing for Envision include a consortium of Carlyle Group LP and TPG Global, the sources added.

The sources asked not to be identified because the matter is confidential. KKR, Carlyle and TPG declined to comment. Envision and HCA did not immediately respond to requests for comment.

Envision announced last year it was reviewing a range of strategic alternatives after reporting disappointing third-quarter earnings, which it attributed partly to the effects of hurricanes Harvey and Irma as well as a slowdown in the growth of patient demand.

Last year, Envision agreed to sell its ambulance unit, AMR, to Air Medical, a medical helicopter business owned by KKR, for $2.4 billion.

The year prior, it merged with AmSurg in an all stock deal that valued the combined companies at the time at around $10 billion. HCA's and KKR's bid would reverse that combination.

A sale of Envision would be the latest in a spate of mergers and acquisitions activity among physician networks, a business that has struggled in recent years to adapt to changes in how U.S. health insurers reimburse providers.

Federal reimbursement programs such as Medicare and Medicaid, for example, have been trying to shift to a "value-based" payment model, whereby providers sometimes receive fixed payments to encourage them to control costs.

Last year, U.S. kidney care-provider DaVita Inc agreed to sell its medical group business, Davita Medical Group, to UnitedHealth Group Inc. for $4.9 billion.

Envision's rival MEDNAX Inc has also been exploring strategic alternatives, including a sale, Reuters has reported.

In 2016, buyout firm Blackstone Group LP acquired hospital staffing provider Team Health Holdings Inc for $6.1 billion.

(Reporting by Joshua Franklin and Carl O'Donnell in New York; Editing by Cynthia Osterman)

By Joshua Franklin and Carl O'Donnell