Bloomberg subsequently reported CVS’s interest.

It couldn’t be learned which other potential buyers might be in the mix, but Cano could be Humana’s to lose as the health insurer has a right of first refusal on any sale, part of an agreement that was originally struck in 2019.

Miami-based Cano operates primary-care centers in California, Florida, Nevada, New Mexico, Texas, Illinois, New York, New Jersey and Puerto Rico, according to documentation from the company. It mainly serves Medicare Advantage members, a private-sector alternative to Medicare for seniors.

Ties between the companies run deep: Cano was Humana’s biggest independent primary-care provider in Florida, serving over 68,000 of its Medicare Advantage members at the end of last year, according to a securities filing. Cano also operated 11 medical centers in Texas and Nevada for which Humana is the exclusive health plan for Medicare Advantage, the filing added.

Humana has already established a footprint in primary care, which it continues to expand. Earlier this year, its CenterWell Senior Primary Care business joined with private-equity firm Welsh, Carson, Anderson & Stowe to open about 100 new senior-focused primary-care clinics between 2023 and 2025, building on an earlier, similar partnership.

At its investor day last week, Humana’s chief executive,

Bruce Broussard,

said that the company sees a total addressable market of over $700 billion in “value-based” primary care for seniors. He noted that Humana has accelerated its investment in the sector over the past five years, becoming the nation’s largest senior-focused primary-care provider.

There has been a frenzy of deal making involving large companies scooping up primary-care assets as a means of getting closer to patients and providing them more personal service.

Amazon.com Inc.

agreed to purchase the parent of primary-care clinic operator One Medical for about $3.9 billion in July, while CVS Health Corp. agreed to buy

Signify Health Inc.

for $8 billion earlier this month.

Cano went public in 2020 through a special-purpose acquisition vehicle backed by real-estate investor

Barry Sternlicht,

who sits on its board. The deal valued the company at $4.4 billion.

Cano has been the target of two shareholder activists this year, both of which independently pushed for its sale.

Dan Loeb’s

Third Point LLC currently has a roughly 5% stake in the healthcare company. In March, he pointed to the market’s unfavorable view of companies that went public through SPACs as a reason to explore strategic alternatives.

Then in late August, Owl Creek Asset Management LP sent a letter to Cano’s board stating that it had amassed a roughly 4% stake and urged the company to hire investment bankers to explore a sale to a strategic buyer.

Cano has been backed by health-care-focused private-equity firm InTandem Capital Partners since 2016. The firm mainly makes investments in small-to-midsize companies.

—Cara Lombardo contributed to this article.

Write to Laura Cooper at laura.cooper@wsj.com and Dana Cimilluca at dana.cimilluca@wsj.com