Franchise Group, which owns brands including Vitamin Shoppe, had offered around $60 a share for Kohl’s, the company said, confirming a prior report by the Journal. It has been vying for the company in competition with private-equity firm Sycamore Partners, which put in a bid in the mid-$50s a share, people familiar with the matter have said.

The stock closed at $42.12 on Monday and rose 13% after hours amid the news.

Shares in Kohl’s, which has said it was exploring strategic options, had fallen about 15% so far this year, buffeted by market turmoil and fears of an economic slowdown, in a decline mitigated by the possibility of a deal.

Weeks ago, Kohl’s had indicated to suitors that it believed the company was worth at least $70 a share, though difficult conditions for retailers and for financing leveraged buyouts might have reined in its price expectations.

Kohl’s, already struggling, was further battered by the Covid-19 pandemic, which ate into sales and wiped out profit in 2020. Sales and profit rebounded in 2021, but by January 2022 the retailer’s stock was worth less than it was two decades ago.

Franchise Group acquires and manages mainly franchise companies.

While it has a market capitalization of just $1.5 billion, there are ways in which the firm could make the purchase more affordable, according to people familiar with the matter, such as by teaming with existing investors or by selling real estate.

—Suzanne Kapner contributed to this article.

Write to Cara Lombardo at cara.lombardo@wsj.com