TALLAHASSEE — A bankruptcy judge is scheduled Tuesday to hold a hearing on Orlando Health’s proposed purchase of three hospitals in Brevard and Indian River counties, after a months-long process that led to the Orlando-based system emerging as the winning bidder.

U.S. Bankruptcy Judge Christopher Lopez is considering a plan for Orlando Health to pay $439 million in cash for Melbourne Regional Medical Center and Rockledge Regional Medical Center in Brevard County and Sebastian River Medical Center in Indian River County, according to court documents.

Orlando Health would buy the hospitals from Steward Health Care, which filed for Chapter 11 bankruptcy in May. Lopez will hold the hearing in Texas, where Steward is based.

A court document filed Sunday said the process of selling the hospitals started in April, when Leerink Partners LLC, an investment-banking advisory firm hired to help market Steward’s assets, contacted dozens of potential buyers to gauge interest. It solicited additional possible bidders after the bankruptcy petition was filed.

The document, a declaration by Toby King, a senior managing director at Leerink, said Orlando Health initially submitted an oral bid in late July and on Aug. 1 submitted a proposal to become what is known as a “stalking horse bidder.” A stalking horse bidder sets an initial bid.

Lopez on Aug. 22 approved Orlando Health’s designation as the stalking horse bidder. The court document said Steward did not receive any other “qualified bids” by an Aug. 26 deadline.

In the declaration, King said he believes there is “sound business justification” for the sale.

“In my opinion, the sale transaction constitutes the best terms available after the completion of a robust and extensive marketing and sale process,” he said in the document. “First and foremost, the sale transaction provides the debtors with significant sale proceeds. Further, the sale transaction was conducted in good faith and is the product of hard-fought, arm’s-length negotiations with the buyer among sophisticated professionals and with the oversight of the debtors’ independent transformation committee.”

Medical Properties Trust, Inc., which owns the hospital properties and leases them to Steward, has raised objections to the Orlando Health deal. The objections stem from unresolved questions about the sale of the real estate.

In addition to the hospitals in Brevard and Indian River counties, Steward owns Coral Gables Hospital, Hialeah Hospital, North Shore Medical Center and Palmetto General Hospital in Miami-Dade County and Florida Medical Center in Broward County. Court documents do not show a successful bidder for those hospitals.

Steward also has operated hospitals in Arizona, Arkansas, Louisiana, Massachusetts, Ohio, Pennsylvania and Texas.