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.

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.

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,