Walgreens Boots Alliance Inc., the troubled drug-store chain in turnaround mode, is exploring options including a sale of Shields Health Solutions, the specialty pharmacy business it acquired a majority of three years ago, according to people familiar with the matter.

The business could be valued at more than $4 billion in a sale, said the people, who asked to not be identified because the details aren’t public. Walgreens is working with advisers to scope out interest in Shields Health, which is expected to draw interest from private equity firms and health-care companies, the people said.