Alden is currently Tribune Publishing's largest shareholder with a 32% stake in the company that owns the Chicago Tribune and New York Daily News, among other media entities.
Alden could buy the rest of the shares it doesn't already own by the end of this month, sources told The Wall Street Journal, though negotiations are still ongoing and could lead to no deal.
Tribune, which has a market capitalization of about $562 million, was up 0.5% to $15.37 in afternoon trading Thursday on the news.
Last year, Alden offered to buy Tribune's shares for $14.25 per share, prompting the company to set up a special board committee of independent directors to review the proposal. The stock has been trading above that level since the negotiations were disclosed.
Two-thirds of shareholders unaffiliated with Alden would have to approve a deal for it to become official.
Billionaire biotech investor Patrick Soon-Shiong owns a 24% stake in the company and former media executive Mason Slaine owns nearly 8%. Slaine has previously indicated that Alden's previous offer was too low, according to the Journal.
The media industry has faced tumultuous times over the last 20 years amid the digital revolution. A Pew Research study suggested that between 2008 and 2019 the media industry cut 51% of its newsroom jobs.
Alden controls MediaNews Group, a private company that owns about 60 daily newspapers across the country. The fund has a reputation for making deep cost cuts at the newspapers it acquires, according to the Journal.