Walgreens Boots Alliance is nearing a deal to sell itself to private equity firm Sycamore Partners for around $10 billion. The transaction could be announced as soon as Thursday, according to people familiar with the matter.

Sycamore Partners is nearing an acquisition of Walgreens Boots Alliance Inc., people with knowledge of the matter said, in a deal that could end the drugstore operator’s tumultuous run as a public company.

Drugstore chain Walgreens Boots Alliance Inc. is closing in on a roughly $10 billion deal to sell itself to Sycamore Partners, a private-equity firm, which would then take Walgreens private and likely break it up,