Deal would cap tumultuous run for retailer whose market value shrank from a peak of over $100 billion to below $8 billion.

If Walgreens Boots Alliance follows through with a sale to private equity, the company might join other healthcare deals under scrutiny for selling out to such investors.

The New York-based private equity firm has been having ongoing discussions about a deal to take Walgreens private, according to people familiar with the matter.