Activist hedge fund Macellum Advisors has been asking Kohl’s to consider selling itself and now it wants at least one seat on the retailer’s board, according to a letter published Tuesday.

Macellum, which owns roughly 5% of Kohl’s stock, said that it also wants Kohl’s to publicly commit to carrying out a process in which it reviews strategic alternatives.

The letter comes a day after Starboard Value-backed Acacia Research confirmed an all-cash offer to buy Kohl’s for $64 a share, or roughly $9 billion, according to a filing with the Securities and Exchange Commission.

Private equity firm Sycamore Partners is also preparing an all-cash offer for Kohl’s at $65 per share, sources told CNBC on Sunday.

Kohl’s shares soared 36% on Monday, closing at $63.71. The stock was down more than 1% in trading Tuesday, amid a broader market sell-off, putting the company’s market cap at about $8.7 billion.

Kohl’s said in a statement Monday that it had received letters expressing interest in acquiring the business, but it didn’t name any potential suitors.

A representative from Kohl’s didn’t immediately respond to CNBC’s request for comment on the latest letter from Macellum.

“We feel the best risk-adjusted path forward for shareholders right now is a credible and open process to evaluate a full sale of the company at an attractive premium,” Macellum’s managing partner, Jonathan Duskin, wrote. “Candidly, we do not have faith in the current Board to run this process on its own.”

Duskin added his firm may take legal action or run another proxy contest if Kohl’s board attempts to chill a sales process.

Macellum is putting the pressure on Kohl’s less than a year after the hedge fund, in a group along with a handful of other activists, reached a deal to add three directors to Kohl’s board.

It contends that Kohl’s has underperformed other off-mall retailers and has mismanaged its business during the Covid pandemic. For example, it criticized Kohl’s for investing too much in athletic apparel over other categories of merchandise.

Hedge fund Engine Capital has also pushed Kohl’s to consider a sale or separate its e-commerce division from its stores, which would mimic a similar move at Saks and something Macy’s is considering.

Since Chief Executive Michelle Gass took the helm of the company in May 2018, Kohl’s has ramped up its links with Amazon and has started adding Sephora shop-in-shops to drive store visits and sales. The company has also been ditching dated apparel brands and stocking its shelves with merchandise from Nike, Under Armour, Cole Haan and Tommy Hilfiger.

In the three-month period ended Oct. 30, Kohl’s revenue climbed to $4.6 billion from $3.98 billion a year earlier. That was slightly below 2019 levels, however.

Find the full letter from Macellum here.

— CNBC’s Leslie Picker contributed to this report.