Staff said they had been warned to expect mass layoffs and that the future of the storied title was unclear.
Sports Illustrated owner Authentic Brands Group said the brand, including "its editorial arm" would live on.
Publisher Arena Group said talks over the licence were ongoing.
"We are in active discussions with Authentic Brands Group ... but we understand we aren't the only ones," a spokeswoman for the company said.
Sports Illustrated launched in 1954 and was for decades a premier title in American sports journalism.
Known for using sports to delve into wider issues, its covers were a coveted spot for athletes and its swimsuit issues regularly sparked commentary.
But, like other magazine and newspapers, it has struggled as eyeballs and advertising shift online.
Authentic Brands Group, which is known for scooping up stressed brands, especially retail names, and licensing them to operators, purchased the title in 2019 for $110m (£85.5m).
It had warned Arena earlier this month that it planned to cancel their deal, after Arena missed a $3.75m payment, according to filings with financial regulators.
"We are committed to ensuring that the traditional ad-supported Sports Illustrated media pillar has best in class stewardship to preserve the complete integrity of the brand's legacy," Authentic Brands said in a statement on Friday..
The spokeswoman for Arena said it would continue to produce Sports Illustrated until the licensing issue was resolved. It also currently owes Authentic a $45m fee due to the cancellation, according to regulatory filings.
"We hope to be the company to take [Sports Illustrated] forward but if not, we are confident that someone will," she said. "If it is another business, we will support with the transition so the legacy of Sports Illustrated doesn't suffer."
Arena, which also puts out smaller titles such as Men's Journal and Parade, has published Sports Illustrated since 2019.
It has presided over job cuts and other turmoil, including a scandal that erupted last year, in which the magazine was accused of publishing articles using artificial intelligence.
The company removed the pieces and launched an investigation. It also said it had licensed the content from another firm, which works with e-commerce companies.
It subsequently fired a slew of executives, including former chief executive Ross Levinsohn, a controversial former executive at Yahoo and Tribune Publishing.
On Thursday, it warned it would be cutting more than 100 jobs - or about one third of its workforce - citing "substantial debt and recently missed payments".
"This is another difficult day in what has been a difficult four years for Sports Illustrated under Arena Group ... stewardship," the union representing staff at Sports Illustrated said on Friday.
It called on Authentic Brands Group to "ensure the continued publication of SI and allow it to serve our audience in the way it has for nearly 70 years".
Arena in August announced it was trying to pull together a deal to be purchased by another media firm.
Shares in the firm, which were trading above $9 a year ago, fell by more than a third to less than $1 on Friday.